Test-Time and Training-Time Reasoning with Code Interpreter
Collection
Model weights and dataset for the paper "Exploring Extrinsic and Intrinsic Properties for Effective Reasoning with Code Interpreter" (TMLR'26) • 8 items • Updated
messages listlengths 4 22 | tools listlengths 1 1 | enable_thinking bool 1
class |
|---|---|---|
[
{
"content": "There are 152 students at Dala High School. Assume the following: \n- 100 students take a Math class \n- 94 students take a Science class \n- 57 students take an English class \n- 73 students take a Math class and a Science class \n- 24 students take a Math class and an English class \n- 27 ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "What is the smallest positive integer that leaves a remainder of 4 when divided by 5 and a remainder of 6 when divided by 7?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Find all triples of three-digit positive integers $x < y < z$ with $x, y, z$ in arithmetic progression and $x, y, z + 1000$ in geometric progression. The original answer is in the form of (k, m, n), please give the value of k + m + n.\n\n[i]For this problem, you may use calculators or computers to... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Let\n$a=\\frac{1^2}{1} + \\frac{2^2}{3} + \\frac{3^2}{5} + \\; \\dots \\; + \\frac{1001^2}{2001}$\nand\n$b=\\frac{1^2}{3} + \\frac{2^2}{5} + \\frac{3^2}{7} + \\; \\dots \\; + \\frac{1001^2}{2003}.$\nFind the integer closest to $a-b$.\n\nRemember to place the final answer in the last part using the... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Find the greatest integer less than $\\sqrt{10} + \\sqrt{80}$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
"tool_calls": null
},
{
"content": "",
"reasonin... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "The legs of a right triangle measure 6 inches and 8 inches. Find the greatest area of a rectangle that can be inscribed in the right triangle( square inches). Give the exact answer\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "ABCDE is a pyramid with square base ABCD. Point E is directly above A with AE = 1024 and AB = 640. The pyramid is cut into two pieces by a horizontal plane parallel to ABCD. This horizontal plane is a distance h above the base ABCD. The portion of ABCDE that is above the plane is a new pyramid. Fo... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "How many pairs of positive integers $(a,b)$ with $a + b \\le 100$ satisfy the equation \\( \\frac{a + \\frac{1}{b}}{\\frac{1}{a} + b} = 13 \\)?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "When the roots of the polynomial \n\n\\[P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \\cdot \\cdot \\cdot (x-10)^{10}\\]\n\nare removed from the number line, what remains is the union of $11$ disjoint open intervals. Find the number of these intervals on which \\( P(x) \\) is positive.\n\nRemember to place the... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Let $a + \\frac{1}{b} = 8$ and $b + \\frac{1}{a} = 3$. Find the sum of the two possible real values for $a$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
"tool_calls": ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "In the figure below, choose point \\(D\\) on \\(\\overline{BC}\\) so that \\(\\triangle ACD\\) and \\(\\triangle ABD\\) have equal perimeters. What is the area of \\(\\triangle ABD\\)?\n\n[asy]draw((0,0)--(4,0)--(0,3)--(0,0)); label(\"$A$\", (0,0), SW); label(\"$B$\", (4,0), ESE); label(\"$C$\", (... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "On the trip home from the meeting where this $AMC~10$ was constructed, the Contest Chair noted that his airport parking receipt had digits of the form $bbcac,$ where $0 \\le a < b < c \\le 9,$ and $b$ was the average of $a$ and $c.$ How many different five-digit numbers satisfy all these propertie... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "What are all values of $p$ such that for every $q>0$, we have $$\\frac{3(pq^2+p^2q+3q^2+3pq)}{p+q}>2p^2q?$$ Express your answer in interval notation in decimal form as [a, b). Please give the value of 2a + 2b.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'T... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "A finite sequence of positive integers $ m_i$ for $ i=1,2,...,2006$ are defined so that $ m_1=1$ and $ m_i=10m_{i-1} +1$ for $ i>1$. Let $ k$ be the number of these integers that are divisible by $ 37$. Find the value of $ k$.\n\nRemember to place the final answer in the last part using the format... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "In a triangle $ABC$, point $D$ lies on $AB$. It is given that $AD = 25$, $BD = 24$, $BC = 28$, and $CD = 20$. Find the length of $AC$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Given a positive integer $n$ , it can be shown that every complex number of the form $r+si$ , where $r$ and $s$ are integers, can be uniquely expressed in the base $-n+i$ using the integers $0,1,2,\\cdots,n^2$ as digits. That is, the equation \n$r+si=a_m(-n+i)^m+a_{m-1}(-n+i)^{m-1}+\\cdots +a_1(-n... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "How many three-digit numbers leave a remainder of $2$ when divided by $5$ and a remainder of $7$ when divided by $9$?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
"tool... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "How many positive integers not exceeding $2001$ are multiples of $3$ or $4$ but not $5$? Provide your answer as an integer.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "The roots of the polynomial \\[x^3 - 52x^2 + 581x - k\\]are distinct prime numbers. Find $k.$\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
"tool_calls": null
},
{
... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Find the minimum value of $n$ such that, among any $n$ integers, there are three whose sum is divisible by $3$.\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "user",
"tool_calls... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Two circles have radii of 5 and 26, respectively. The smaller circle passes through the center of the larger one. What is the difference between the lengths of the longest and shortest chords of the larger circle that are tangent to the smaller circle?\n\nRemember to place the final answer in the ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Find the value of \\(i + 2i^2 + 3i^3 + \\ldots + 2002i^{2002}\\). The original answer is in the form of \\(k + mi\\), please give the value of \\(k + m\\).\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Find the largest constant $m,$ so that for any positive real numbers $a,$ $b,$ $c,$ and $d,$\n\\[\\sqrt{\\frac{a}{b + c + d}} + \\sqrt{\\frac{b}{a + c + d}} + \\sqrt{\\frac{c}{a + b + d}} + \\sqrt{\\frac{d}{a + b + c}} > m.\\]\n\nRemember to place the final answer in the last part using the format... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Let $S$ be the set of 10-tuples $(a_0, a_1, \\dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples. For each 10-tuple $s = (a_0, a_1, \\dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that\n\\[p_s(n) = a_n\\]for $0 \\le n \\le 9.$ For example, $... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "Find all functions f from the set of real numbers into the set of real numbers which satisfy for all real $x,y$ the identity\n$f(xf(x+y))=f(yf(x))+x^2.$\nThe original answer is in the form of af(x) and bf(x), please give the value of a + b.\n\nRemember to place the final answer in the last part us... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "How many pairs of positive integers $(a,b)$ are there such that ${gcd}(a,b)=1$ and $\\frac{a}{b} + \\frac{14b}{9a}$ is an integer?\n\nRemember to place the final answer in the last part using the format: \n\n\\boxed{{'The final answer goes here.'}}",
"reasoning_content": null,
"role": "use... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
[
{
"content": "A fair, twenty-faced die has $19$ of its faces numbered from $1$ through $19$ and has one blank face. Another fair, twenty-faced die has $19$ of its faces numbered from $1$ through $8$ and $10$ through $20$ and has one blank face. When the two dice are rolled, what is the probability that the sum ... | [
{
"function": {
"description": "A tool for executing code.",
"name": "code_interpreter",
"parameters": {
"properties": {
"code": {
"description": "The code to execute.",
"type": "string"
}
},
"required": [
"code"
... | true |
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