TRICE: Models and Datasets
Collection
3 items • Updated
prompt listlengths 1 1 | label listlengths 1 1 | messages listlengths 2 142 | tools listlengths 1 1 ⌀ | metadata unknown |
|---|---|---|---|---|
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the integral $\\int \\sqrt{\\cos(x)} \\, dx$."
}
] | [
"\\;\n \\int\\sqrt{\\cos x}\\,dx\n =\\sin x\\;{}_2F_{1}\\!\\Big(\\frac12,\\frac14;\\frac32;\\sin^{2}x\\Big)+C\n =\\frac12\\,B_{\\sin^{2}x}\\!\\Big(\\frac12,\\frac14\\Big)+C\n \\;"
] | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the integral $\\int \\sqrt{\\cos(x)} \\, dx$."
},
{
"role": "assistant",
"reasoning_content": "We need to compute indefinite integral \\int sqrt(cos x) dx. This... | [
{
"type": "function",
"function": {
"name": "python",
"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 20.0 seconds.",
"parameters": {
"type": "object",
... | {
"points": [
1
],
"source": "aops",
"difficulty": {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 7,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
"pass": 0,
... |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCalculate the sum:\n\\[ 2\\begin{pmatrix}\n\\cos \\frac{\\pi }{3} & -\\sin \\frac{\\pi }{3} \\\\ \\sin \\frac{\\pi }{3}\n & \\cos \\frac{\\pi }{3}\n\\end{pmatrix}+ 4\\begin{pmat... | [
"\n\\frac{2^{\\,n+1}}{\\sqrt3}\n\\begin{pmatrix}\n\\sin\\frac{(n+1)\\pi}{3}&\\cos\\frac{(n+1)\\pi}{3}\\\\[2pt]\n-\\cos\\frac{(n+1)\\pi}{3}&\\sin\\frac{(n+1)\\pi}{3}\n\\end{pmatrix}\n-\n\\begin{pmatrix}\n1&\\dfrac{1}{\\sqrt3}\\\\[2pt]\n-\\dfrac{1}{\\sqrt3}&1\n\\end{pmatrix}"
] | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCalculate the sum:\n\\[ 2\\begin{pmatrix}\n\\cos \\frac{\\pi }{3} & -\\sin \\frac{\\pi }{3} \\\\ \\sin \\frac{\\pi }{3}\n & \\cos \\frac{\\pi }{3}\n\\end{pmatrix}+ 4\\begin{pmat... | [
{
"type": "function",
"function": {
"name": "python",
"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 20.0 seconds.",
"parameters": {
"type": "object",
... | {
"points": [
1
],
"source": "aops",
"difficulty": {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 7,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
"pass": 0,
... |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( g \\) be the harmonic mean of the arithmetic mean of the geometric mean of \\( abc \\) and \\( def \\) and the arithmetic mean of \\( ace \\) and \\( bdf \\). Compute \\... | [
"\\displaystyle \ng=\\frac{2\\sqrt{a b c d e f}\\,\\bigl(a c e+b d f\\bigr)}\n{2\\sqrt{a b c d e f}+a c e+b d f}"
] | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( g \\) be the harmonic mean of the arithmetic mean of the geometric mean of \\( abc \\) and \\( def \\) and the arithmetic mean of \\( ace \\) and \\( bdf \\). Compute \\... | [
{
"type": "function",
"function": {
"name": "python",
"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 20.0 seconds.",
"parameters": {
"type": "object",
... | {
"idx": 10841,
"points": [
1
],
"source": "aops",
"difficulty": {
"reason_low_with_tool": {
"count": 8,
"pass": 1,
"accuracy": 0.125
},
"reason_low_no_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
... |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn $\\triangle ABC$ with angles $\\alpha, \\beta, \\gamma$, angle $\\gamma$ is trisected, with the trisectors meeting $AB$ at points $D$ and $E$, where $D$ is closer to $A$. If ... | [
"AD:DE:EB\\;=\\;\\sin^{2}\\beta\\;:\\;2\\sin\\alpha\\sin\\beta\\cos\\!\\Bigl(\\frac{\\gamma}{3}\\Bigr)-\\sin^{2}\\beta\\;:\\;\\sin^{2}\\alpha"
] | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn $\\triangle ABC$ with angles $\\alpha, \\beta, \\gamma$, angle $\\gamma$ is trisected, with the trisectors meeting $AB$ at points $D$ and $E$, where $D$ is closer to $A$. If ... | [
{
"type": "function",
"function": {
"name": "python",
"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 20.0 seconds.",
"parameters": {
"type": "object",
... | {
"points": [
1
],
"source": "aops",
"difficulty": {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
"pass": 0,
... |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSpin a regular coin repeatedly until both heads and tails have appeared $k$ times ($k = 1, 2, \\dots$). Denote by $v_k$ the number of necessary throws. Find the distribution of ... | [
""
] | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSpin a regular coin repeatedly until both heads and tails have appeared $k$ times ($k = 1, 2, \\dots$). Denote by $v_k$ the number of necessary throws. Find the distribution of ... | [
{
"type": "function",
"function": {
"name": "python",
"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 20.0 seconds.",
"parameters": {
"type": "object",
... | {
"points": [
1
],
"source": "aops",
"difficulty": {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 8,
"pass": 1,
"accuracy": 0.125
},
"reason_medium_with_tool": {
"count": 8,
"pass": 0,
... |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the integer solutions of $\\frac{x+y}{y+z} = \\frac{x+z}{x+y}$."
}
] | [
"\n\\begin{aligned}\nx&=\\frac{\\varepsilon\\,k\\,pq+ k\\,q^{2}-k\\,p^{2}}{2}\n =\\frac{k\\bigl(\\varepsilon pq+q^{2}-p^{2}\\bigr)}{2},\\\\[2mm]\ny&=\\frac{\\varepsilon\\,k\\,pq+ k\\,p^{2}-k\\,q^{2}}{2}\n =\\frac{k\\bigl(\\varepsilon pq+p^{2}-q^{2}\\bigr)}{2},\\\\[2mm]\nz&=\\frac{k\\bigl(p^{2}+q^{2}-\\varep... | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the integer solutions of $\\frac{x+y}{y+z} = \\frac{x+z}{x+y}$."
},
{
"role": "assistant",
"reasoning_content": "We need integer solutions (x,y,z) presumably in... | [
{
"type": "function",
"function": {
"name": "python",
"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 20.0 seconds.",
"parameters": {
"type": "object",
... | {
"points": [
1
],
"source": "aops",
"difficulty": {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
"pass": 1,
... |
[{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | ["\\displaystyle \nI(a)=-\\operatorname{Im}\\!\\bigl[e^{\\,ia}\\,E_{1}(ia)\\bigr]\n =\\operator(...TRUNCATED) | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [{"type":"function","function":{"name":"python","description":"Call this function to execute Python (...TRUNCATED) | {"points":[1.0],"source":"aops","difficulty":{"reason_low_with_tool":{"count":8,"pass":0,"accuracy":(...TRUNCATED) |
[{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | ["\\displaystyle\n\\int_{0}^{t}\\sqrt{1+x^{4}}\\,dx\n= \\frac{t}{3}\\sqrt{1+t^{4}}\n +\\frac13\\Bi(...TRUNCATED) | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [{"type":"function","function":{"name":"python","description":"Call this function to execute Python (...TRUNCATED) | {"points":[1.0],"source":"aops","difficulty":{"reason_low_with_tool":{"count":8,"pass":0,"accuracy":(...TRUNCATED) |
[{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"\\,K\n =\\sqrt{s\\,(s-p)\\,(s-q)\\,\\bigl(s-(a+b)\\bigr)}\\;"
] | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [{"type":"function","function":{"name":"python","description":"Call this function to execute Python (...TRUNCATED) | {"points":[1.0],"source":"aops","difficulty":{"reason_low_with_tool":{"count":8,"pass":0,"accuracy":(...TRUNCATED) |
[{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | ["\n\\begin{cases}\n(x,y)=(n,0) &\\text{with }n\\ge 0,\\\\[4pt]\n(x,y)=(0,-1),\\\\[4pt]\n(x,y)=(-4k^(...TRUNCATED) | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [{"type":"function","function":{"name":"python","description":"Call this function to execute Python (...TRUNCATED) | {"points":[1.0],"source":"aops","difficulty":{"reason_low_with_tool":{"count":8,"pass":0,"accuracy":(...TRUNCATED) |
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