
555 F.3d 659 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Natasha L. GENTRY, Defendant-Appellant.
No. 07-3361.
United States Court of Appeals, Eighth Circuit.
Submitted: April 17, 2008.
Filed: February 9, 2009.
*661 Stephen C. Moss, Asst. Fed. Public Defender, Kansas City, MO, argued (Raymond C. Conrad, Jr., Fed. Public Defender, on the brief), for appellant.
Charles E. Ambrose, Asst. U.S. Atty., Kansas City, MO, argued (John W. Wood, U.S. Atty., Amy B. Marcus, Asst. U.S. Atty., on the brief), for appellee.
Before LOKEN, Chief Judge, JOHN R. GIBSON, and MELLOY, Circuit Judges.
JOHN R. GIBSON, Circuit Judge.
Natasha Gentry was convicted of one count of possession with intent to distribute methamphetamine and one count of carrying a gun during a drug trafficking offense. On appeal she argues that the district court erred in allowing the government to elicit testimony concerning her post-arrest silence which violated her due process rights. She also argues that the government failed to produce evidence sufficient to support the verdict and that the court violated her substantive rights when it refused to give a jury instruction on the lesser included offense of simple possession of methamphetamine. We reverse and remand for a new trial.
On August 31, 2005, private security guards drove to an apartment building at 2732 Charlotte in Kansas City, Missouri to serve an eviction. When the security guards arrived, they saw a white Cadillac parked in the lot. One of the guards saw a man run away from the car. After the Cadillac left, the guards discovered a plastic baggie of methamphetamine on the ground where the car had been parked. When the Cadillac pulled back into the parking lot while the guards were waiting for police to arrive, the guards surrounded the car and ordered the driver, Natasha Gentry, to get out of the car. Police officers searched the car after they arrived and found various chemicals and equipment associated with the production of methamphetamine, including starter fluid, a funnel, coffee filters, rubber tubing, and ephedrine. The officers also discovered several firearms in the car and a glass pickle jar containing a cloudy white substance. *662 The substance later tested positive for the presence of methamphetamine.
The jury convicted Gentry of aiding and abetting in the possession with intent to distribute 50 grams or more of methamphetamine, and of carrying a firearm in relation to a drug trafficking offense. The district court granted her motion for judgment of acquittal on one count of conspiracy in relation to the other offenses.

I.
Gentry was arrested at the scene and was taken to a police station. While she was in custody, a detective asked her a series of biographical question and gave her a Miranda[1] warning. Gentry invoked her right to counsel and chose to stop the questioning. At trial, Gentry's counsel objected to a line of questions during Gentry's cross-examination regarding her silence after being Mirandized. She argues that the evidence elicited of her post-Miranda-warning silence violated her due process rights and is reversible error. We review claims of constitutional error de novo. United States v. Washington, 318 F.3d 845, 854-55 (8th Cir.2003).
The record reveals that the prosecution made a number of inquiries and comments during Gentry's cross-examination regarding her post-arrest silence and request for counsel:
Q: Now, at that time [after being arrested] you didn't volunteer [to Detective Manley] that that baggie was  that didn't belong to you, did you?
A: No. But I don't believe he asked me. Basically he asked me [for biographical data]. And then he advised me that anything I say can and will be used against me in the court of law, and that I was being charged with the things found in that vehicle. At that point and time I remained quiet..
Q: But you didn't at that point volunteer, like you had previously to the security guards, that that wasn't your baggie or ... those weren't your drugs, that wasn't your car?
...
A: Like I had said, he had told me anything that I say to him can and will be used against me and at that point I remained quiet. I asked him, I believe,... that I would like an attorney to be present with me before I speak.
...
Q: [O]nce this case was preparing for trial, ... was the first time that you told your defense attorney about the identity of Rocky Johnson,[2] isn't that right?
A: He was my attorney. Yes, ma'am.
Q: And you'd never told anyone else before about Rocky Johnson being present at the scene or anything like that up to that point, isn't that right?
...
Q: And you didn't say that later either when you were being treated politely and being asked for basic information. You didn't volunteer that at that time either, did you?
A: No, I didn't. But at that point he had let me know what my rights were and what would happen.
Q: And, in fact, Rocky Johnson's name didn't even come up until you had *663 counsel and this case was being prepared for trial, isn't that right?
In its closing argument, the government again raised Gentry's post-arrest silence: "[I]f, as she said, she told the security guards initially that that wasn't her dope in the car, that that wasn't her stuff, why... not later profess that to the officers at the scene or the detective? Why wait for a full year until this case is going to trial and deprive law enforcement of the ability to track down others who she says ... it's their dope ...?" (emphasis added).
In Doyle v. Ohio, 426 U.S. 610, 619, 96 S.Ct. 2240, 49 L.Ed.2d 91 (1976), the Court held that it was a violation of due process to impeach a defendant with her post-arrest silence. In Doyle, after the defendants were arrested and Mirandized, they declined to give statements to the police. Id. at 612, 96 S.Ct. 2240. At trial the defendants testified that they had been framed, and on cross-examination the government asked the defendants about their failure to tell the police that they were framed when they were arrested. Id. at 613-14, 96 S.Ct. 2240. The Court held that silence after Miranda warnings was "insolubly ambiguous" because it may be induced by the warning itself: "[I]t would be fundamentally unfair and a deprivation of due process to allow the arrested person's silence to be used to impeach an explanation subsequently offered at trial." Id. at 617-18, 96 S.Ct. 2240. See also Wainwright v. Greenfield, 474 U.S. 284, 295 n. 13, 106 S.Ct. 634, 88 L.Ed.2d 623 (1986) ("[S]ilence does not mean only muteness; it includes the statement of a desire to remain silent, as well as of a desire to remain silent until an attorney has been consulted."); Fields v. Leapley, 30 F.3d 986, 990 (8th Cir.1994) (same).
In its brief, the government characterizes the cross-examination of Gentry as impeachment based on her prearrest silence and prior inconsistent statements. To the extent that the cross-examination addressed what Gentry told or did not tell the private security guards prior to her arrest, it was not a violation of due process. Under a generous view, the prosecutor's questions to Gentry about whether she ever told "anyone" certain pieces of exculpatory information, were intended to inquire into her prearrest silence.
However, the examination went further than this and inquired into Gentry's silence when she was interrogated by Detective Manley after her arrest. The government asked Gentry direct questions about her silence and elicited responses regarding her requests for counsel. The government cites Kibbe v. DuBois, 269 F.3d 26, 34 (1st Cir.2001), for the proposition that if a defendant claims to have told the police exculpatory information on arrest, she may be cross-examined on her silence. In Kibbe, the defendant claimed at trial to have told the police "all matters concerning the charge for which he was arrested." Id. at 31. Gentry did not claim at trial that she told the police about Rocky Johnson at the time of her arrest. Thus, her post-arrest silence was not a proper subject of examination.
At oral argument the government acknowledged that the line of questions regarding Gentry's post-arrest silence was in error but argued that it was not prejudicial. A Doyle violation is reversible error unless it is harmless beyond a reasonable doubt. See United States v. Martin, 391 F.3d 949, 955 (8th Cir.2004).
When analyzing whether Doyle violations are harmless beyond a reasonable doubt, this court examines (1) whether the government made repeated Doyle violations, (2) whether any curative effort was made by the trial court, (3) whether the defendant's exculpatory evidence is transparently frivolous, and (4) *664 whether the other evidence of the defendant's guilt is otherwise overwhelming.
Fields v. Leapley, 30 F.3d 986, 991 (8th Cir.1994) (internal quotation marks omitted).
With regard to the first factor, repeated violations, we hold that there were at least five separate Doyle violations: Testimony was elicited regarding Gentry's request for an attorney after she was given Miranda warnings; Gentry was asked at least three times about her silence after the Miranda warnings; and, in closing, the government commented on Gentry's silence in her conversation with Detective Manley. The record suggests that cross-examination on Gentry's post-arrest silence made an impact on the jury. Following Gentry's examination, the jury asked her, "And what took you so long to get Rocky Johnson involved?"[3] As to the second factor, no curative instruction was given; the court overruled the objections made by Gentry's counsel.
Third, the theory presented by the defense cannot be said to be "transparently frivolous." The defense argued at trial that the items seized from the car belonged to Rocky Johnson. This theory, which was supported by the testimony of several defense witnesses, was not directly contradicted by the testimony of any government witnesses. With respect to the fourth factor, the evidence of Gentry's guilt is not "otherwise overwhelming." There was significant dispute regarding whether Gentry possessed the materials in the car and whether she had an intent to distribute. Given that Gentry's credibility was vital to the jury's resolution of these issues, we cannot agree with the government's contention that there was no prejudice to Gentry.
We consider Gentry's other arguments because they are relevant on remand.

II.
Gentry argues that the evidence presented at trial was insufficient to convict her for possession with intent to distribute a quantity of methamphetamine greater than 50 grams under 21 U.S.C. § 841. We review a challenge to the sufficiency of evidence de novo, considering the evidence in the light most favorable to the government. United States v. Brooks, 174 F.3d 950, 954 (8th Cir.1999). When a sufficiency argument hinges on the interpretation of a statute, we review the district court's statutory interpretation de novo. United States v. Williams, 136 F.3d 547, 550 (8th Cir.1998).

A.
Gentry first contends that the liquid solution that she possessed was not properly a "mixture or substance" of methamphetamine under 21 U.S.C. § 841(b)(1)(B)(viii)[4] due to its toxic, unusable, and unmarketable state. Thus, Gentry argues, the full weight of the liquid should not be used to determine whether she is subject to a mandatory minimum sentence. The government responds (1) *665 that the market-oriented approach to § 841 includes liquid solutions of methamphetamine created during manufacturing, since that is a step necessary to creating drugs for the market, and (2) that the solution recovered is a "mixture or substance" under the plain meaning of those words.
Kansas City Police recovered 92.07 grams of a cloudy liquid from a pickle jar found in the vehicle Gentry was driving. Several tests of the liquid returned results positive for the presence of methamphetamine. The chemist who performed the tests also testified that he believed that the liquid was produced using the lithium-ammonia method because it had a "strong ammonia smell." A narcotics detective testified that, "at the stage [the liquid] was in," he did not believe that it was usable methamphetamine. He stated that the liquid was corrosive and had a chemical smell. Further, he testified that the majority of users would not know how to manufacture methamphetamine and that "they're just scared to death of it because of the ... chance for explosions."
In their discussion of the argument, both sides focus on the analysis of the words "mixture or substance" in Chapman v. United States, 500 U.S. 453, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991). In Chapman, the Court reviewed a conviction for distribution of LSD. The lower court used the combined weight of the LSD and the blotter paper used to distribute single doses of LSD on the market to calculate sentences. As a result, the district court imposed the mandatory minimum sentence under § 841. Id. at 455, 111 S.Ct. 1919. The Court examined sentencing schemes for other drugs and noted that "[i]nactive ingredients are combined with pure heroin or cocaine, and the mixture is then sold to consumers as a heavily diluted form of the drug." Id. at 460, 111 S.Ct. 1919. Accordingly, the court held that blotter paper customarily used to distribute LSD is a "mixture or substance containing a detectable amount of LSD" for the purposes of § 841. Id. at 461, 111 S.Ct. 1919. In coming to its conclusion, the Court focused on how LSD is marketed in the custom of the drug trade. Id. at 466, 111 S.Ct. 1919 ("Blotter paper seems to be the carrier of choice, and the vast majority of cases will therefore do exactly what the sentencing scheme was designed to do  punish more heavily those who deal in larger amounts of drugs.").
The Eighth Circuit addressed the issue of whether a toxic liquid solution of methamphetamine is a "mixture or substance" for the purposes of § 841 in United States v. Kuenstler, 325 F.3d 1015 (8th Cir.2003). In Kuenstler, authorities seized approximately 92 grams of a solution that contained methamphetamine from a lab in the attic of a house. Id. at 1018 ("0.53 grams of solid material and 91.9 grams of liquid"). The defendants were convicted of two charges related to manufacturing methamphetamine in an amount of fifty grams or more, and they appealed their sentences on the grounds that the "unusable and unmarketable" solutions were not "mixtures or substances" within the meaning of the statute. Id. at 1019. This court held that the total weight of the solution, not just the weight of the solid methamphetamine, should be counted under § 841. Id. at 1023. Applying the Chapman market-oriented rationale, this court concluded that it supported the classification of the liquid solution as a "mixture or substance": "The market for this type of methamphetamine is based on its manufacture in labs like that of the conspirators, and that process involves creation of liquid solutions like those seized here, a process that results in a product for distribution." Id.
*666 Gentry attempts to distinguish Kuenstler on the grounds that Kuenstler was a manufacturing case rather than a distribution case. She urges us to apply a different rule for determining whether toxic solutions are a "mixture or substance" depending on whether the defendant was charged with distribution or manufacturing. The argument is that the market-oriented analysis makes the unusable toxic liquid solution of methamphetamine a "mixture or substance" for the purpose of manufacturing because this type of methamphetamine is based on its manufacture in a process that only later results in a product for distribution. The statute makes no distinction in what constitutes a "mixture or substance" based on the charged conduct. It applies equally to manufacturing, distributing, or dispensing, or possessing with intent to manufacture, distribute or dispense, a controlled substance. 21 U.S.C. § 841(a)(1). Kuenstler is controlling precedent that we are not free to disregard in favor of decisions Gentry cites from other circuits which limit the relevant weight to the actual methamphetamine.
Chapman holds that the ordinary meaning of "mixture or substance" includes two or more components that are commingled yet retain a separate existence. 500 U.S. at 462-63, 111 S.Ct. 1919. The solution that Gentry possessed was made up of a combination of chemicals that contained methamphetamine. Thus, the full weight of the liquid in the pickle jar, 92.07 grams, may be counted for purposes of § 841 and the evidence is sufficient to support the imposition of the mandatory minimum sentence.

B.
Next, Gentry contends that there is insufficient evidence to show that she had the requisite specific intent to distribute the methamphetamine in the pickle jar. The government argues that there is adequate circumstantial evidence of intent to support the jury's finding, including the handguns and a baggie of methamphetamine found at the scene.
At the time of her arrest, Gentry possessed the pickle jar with its liquid solution of methamphetamine. The government's undisputed evidence showed that this liquid was toxic, presently unusable, and posed a threat of emitting harmful chemical gasses or potential explosions. Gentry argues that she could not be shown to have the requisite intent to distribute the methamphetamine because the liquid was unusable and unmarketable. Gentry also contends that the small amount of usable methamphetamine that could be produced from the liquid is consistent with personal use, not distribution. The liquid recovered from the pickle jar was not tested to determine how much usable methamphetamine it could produce. At oral argument, the parties agreed that the quantity of liquid possessed by Gentry would likely produce 1 gram of powder methamphetamine  a user quantity.
The evidence shows that Gentry possessed a handgun. The government also introduced evidence of a bag containing approximately 24.30 grams of powder methamphetamine.[5] Circumstantial evidence such as the presence of a firearm or *667 a large quantity of drugs may be used to prove intent to distribute. See United States v. Brett, 872 F.2d 1365, 1370 (8th Cir.1989). Additionally, the fact that the methamphetamine in the bag was further subdivided into seven Ziploc baggies, supports a finding of intent to distribute. See United States v. Kuenstler, 325 F.3d 1015, 1024 (8th Cir.2003) (holding evidence sufficient to support conviction of intent to distribute based on, inter alia, 0.47 grams of methamphetamine divided into five individual packages).
We sit as a reviewing court, not as a trier of fact. Were we to evaluate this evidence in the first instance, we may have found Gentry's arguments to be persuasive. Viewing the evidence in the light most favorable to the government, we cannot say that the evidence in this case was legally insufficient to prove intent to distribute.

III.
The next issue raised by Gentry is that she was entitled to a jury instruction on the lesser included offense of simple possession of methamphetamine. The government contends that the evidence would not permit a rational jury to acquit Gentry of possession with intent to distribute methamphetamine but convict her of the lesser included offense.
We review the district court's instructions to the jury for abuse of discretion. A defendant is entitled to an instruction on a lesser included offense if all of these elements are present: (1) a proper request is made; (2) the elements of the lesser offense are identical to part of the elements of the greater offense; (3) there is some evidence which would justify conviction of the lesser offense; (4) the proof on the element or elements differentiating the two crimes is sufficiently in dispute so that the jury may consistently find the defendant innocent of the greater and guilty of the lesser included offense; and (5) there is mutuality, i.e., a charge may be demanded by either the prosecution or the defense. United States v. Parker, 32 F.3d 395, 400-01 (8th Cir.1994) (quoting United States v. Thompson, 492 F.2d 359, 362 (8th Cir.1974)).
There is no dispute over elements 1, 2 and 5. The defense requested the lesser included offense instruction at trial; the trial court refused to give it. Possession of a controlled substance, 21 U.S.C. § 844, is a lesser included offense of possession of a controlled substance with intent to distribute, 21 U.S.C. § 841(a)(1). See United States v. Brischetto, 538 F.2d 208, 209 (8th Cir.1976) ("An essential element of the offense covered by the indictment is proof of intent to distribute. Such proof is not required for a conviction under 21 U.S.C. § 844 covered by the requested instruction."). Our task is to determine whether there is some evidence that would justify a conviction on a count of simple possession, and whether the proof of Gentry's intent is sufficiently in dispute so that the jury may have found her innocent of possession with intent to distribute but guilty of simple possession.
The third element is satisfied by the evidence produced at trial that Gentry was alone in the car with a jar of liquid methamphetamine next to her. Such evidence would support a conviction of simple possession.
The fourth element requires a more in-depth analysis of the evidence of intent to distribute. As discussed above, there was evidence presented by both government and defense witnesses that casts doubt on Gentry's intent to distribute the liquid methamphetamine. Although the evidence presented at trial was sufficient to support Gentry's conviction for possession with intent *668 to distribute, the standard here is more searching. We evaluate the evidence to determine whether a trier of fact could have rationally found that Gentry only possessed the methamphetamine, rather than possessed it with intent to distribute, if given an instruction to consider the lesser charge. See Brischetto, 538 F.2d at 210 (reversing for new trial when "[a] rational basis exists for the jury to convict the defendant on the possession charge and acquit him on the intent to distribute charge").
Here, the facts that Gentry enumerates in her brief have more weight. The testimony of Detective Manley establishes that methamphetamine is usually a grainy or crystal substance, and that the liquid methamphetamine seized in this case would not be sold on the street. In this context, courts have looked for evidence that the defendant is a user or may have intended to use the controlled substance. We find that there is some evidence that Gentry intended to use the methamphetamine that she possessed, particularly because she possessed only a small amount. Detective Manley testified that a typical user amount of methamphetamine is one gram, and that a user may also buy a "teenager" (1.75 grams) or an "eight ball" (3.45 grams). The government repeatedly characterizes the evidence as showing that Gentry possessed 92.07 grams of liquid methamphetamine. While this total amount may be used for the purpose of a mandatory minimum sentence under 21 U.S.C. § 841, we need not accept it as equivalent to 92 grams of powder methamphetamine for this analysis. The liquid was not tested to determine how much methamphetamine it contained, but the government conceded that it would likely produce around 1 gram, which is a user amount. The facts distinguish this case from the cases the government relies on in which the lesser included instruction was properly refused when the defendant possessed quantities exponentially greater than the user amount. See, e.g., Parker, 32 F.3d at 397 (greater than 100 grams of powder methamphetamine).
The government cites two cases, United States v. Dodd, 473 F.3d 873 (8th Cir.), cert. denied, ___ U.S. ___, 127 S.Ct. 2280, 167 L.Ed.2d 1114 (2007), and United States v. Ziesman, 409 F.3d 941 (8th Cir. 2005), in support of its contention that the evidence of Gentry's intent to distribute was so overwhelming that it was not sufficiently in dispute to justify the lesser included charge. In Dodd, the government produced nine witnesses who testified that Dodd sold cocaine or was involved in its distribution. Other evidence showed that he sold a large quantity of cocaine that was of a purity consistent with distribution. 473 F.3d at 876-77. And, at the time of Dodd's arrest, a scale used to weigh drugs and packaging material "of the type used to package crack cocaine" was recovered. Id. at 875. However, Dodd presented some testimonial evidence that he was a drug user, which he used to argue that the jury could rationally have found that he intended personal use of the controlled substances that he possessed. Id. at 877. The court concluded that Dodd was not entitled to the lesser-included-offense instruction since it "would [have been] irrational for a jury to disregard the overwhelming evidence ... [of] conspiracy to distribute the cocaine." Id. In Ziesman, the court similarly concluded that no rational jury could have found the defendant innocent of the greater manufacturing charge but guilty of the lesser possession charge. The court held that "extensive physical evidence of the methamphetamine lab at [Ziesman's] farmhouse" and numerous witnesses to the manufacturing would make it irrational for a jury to conclude that Ziesman only possessed, *669 but did not manufacture, methamphetamine. 409 F.3d at 950.
Here, the government contends that the pickle jar, coffee filters and other manufacturing-related items in the car and the gun in Gentry's suitcase constitute "overwhelming" physical evidence of intent to distribute. While the presence of a gun in the proximity of drugs may support a finding of intent to distribute, United States v. Brett, 872 F.2d 1365, 1370 (8th Cir.1989), it does not compel such a finding. Additionally, the other physical evidence would be more probative of a manufacturing charge than of the distribution charge that Gentry faced. We hold that the physical evidence in this case is significantly less compelling than the independent physical evidence in Dodd and Ziesman. There was also no direct evidence of Gentry's specific intent, as there was in the cases cited by the government. The evidence presented leaves the issue of Gentry's intent to distribute "sufficiently in dispute so that the jury may consistently find [her] innocent of the greater and guilty of the lesser included offense." See Parker, 32 F.3d at 401 (internal citation omitted). Thus, on remand Gentry is entitled to a jury instruction of possession of a controlled substance under 21 U.S.C. § 844.
Gentry's conviction is reversed and this cause is remanded for a new trial not inconsistent with this opinion.
NOTES
[1]  Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).
[2]  Gentry's defense theory was that the drugs and other materials found in the car belonged to Rocky Johnson.
[3]  The district court permitted the jury to pose questions to the witnesses after the examinations were completed.
[4]  The statute imposes a 5-year mandatory minimum sentence for violations of § 841(a)(1), which makes it unlawful to knowingly or intentionally "manufacture, distribute, or dispense, or possess with intent to manufacture, distribute, or dispense, a controlled substance," based on methamphetamine quantity as follows: "5 grams or more of methamphetamine, its salts, isomers, and salts of its isomers or 50 grams or more of a mixture or substance containing a detectable amount of methamphetamine, its salts, isomers, or salts of its isomers." 21 U.S.C. § 841(b)(1)(B)(viii).
[5]  Gentry argues that reliance on the baggie of powder methamphetamine to support her conviction is a constructive amendment and the evidence cannot be used to support her conviction. Gentry did not preserve this argument below and it is made for the first time in her reply brief, so it has been waived. United States v. Greene, 513 F.3d 904, 906-7 (8th Cir.2008) (an argument raised for the first time on reply has been waived and will not be addressed).
