conversations listlengths 2 2 | question stringlengths 8 4.04k ⌀ | source stringclasses 8
values | id int64 3 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 811 ⌀ | prompt_type stringclasses 2
values | model_responses__example_annotation listlengths 2 2 | model_responses__example_annotation__finish_reason_length_flags listlengths 2 2 | model_responses__example_annotation__length_partial_responses listlengths 2 2 | prompt__example_annotation__metadata dict | model_responses__example_annotation__metadata dict |
|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "In the geometric sequence $\\{a\\_n\\}$, $a\\_n > 0 (n \\in \\mathbb{N}^*)$ and $a\\_4 = 4$, $a\\_6 = 16$. The common ratio $q$ of the sequence $\\{a\\_n\\}$ is $(\\ \\ \\ \\ )$.\nA: $1$\nB: $2$\nC: $3$\nD: $4$"
},
{
"from": "assistant",
"value": "<think>\nAlright, le... | In the geometric sequence $\{a\_n\}$, $a\_n > 0 (n \in \mathbb{N}^*)$ and $a\_4 = 4$, $a\_6 = 16$. The common ratio $q$ of the sequence $\{a\_n\}$ is $(\ \ \ \ )$.
A: $1$
B: $2$
C: $3$
D: $4$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | B | rephrase | [
"Rewritten Question: In a geometric sequence where \\(a_n > 0\\) for all \\(n \\in \\mathbb{N}^*\\), given \\(a_4 = 4\\) and \\(a_6 = 16\\), find the common ratio \\(q\\).\n\nStep 1: Express \\(a_4\\) and \\(a_6\\) in terms of the first term \\(a_1\\) and the common ratio \\(q\\).\n- For \\(a_4\\): \\(a_4 = a_1 q^3... | [
false,
false
] | [
"",
""
] | {
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"backend": "litellm",
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"generation_params": {
"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "7. If a non-zero complex number $x$ satisfies $x+\\frac{1}{x}=1$, then $x^{2014}+\\frac{1}{x^{2014}}=$ $\\qquad$ ."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of \\( x^{2014} + \\frac{1}{x^{2014}} \\) given that \\( x + \\frac{1}{x}... | 7. If a non-zero complex number $x$ satisfies $x+\frac{1}{x}=1$, then $x^{2014}+\frac{1}{x^{2014}}=$ $\qquad$ . | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | -1 | rephrase | [
"Rewritten Question: If a non-zero complex number \\( x \\) satisfies \\( x + \\frac{1}{x} = 1 \\), find \\( x^{2014} + \\frac{1}{x^{2014}} \\).\n\nStep 1: Solve for \\( x \\).\nGiven \\( x + \\frac{1}{x} = 1 \\), multiply both sides by \\( x \\):\n\\[ x^2 + 1 = x \\]\nRearrange into standard quadratic form:\n\\[ x... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
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"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "A motel bills its customers by charging a flat fee for the first night and then adding on a fixed amount for every night thereafter. If it costs George $\\$155$ to stay in the motel for 3 nights and Noah $\\$290$ to stay in the motel for 6 nights, how much is the flat fee for the... | null | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 65 | rephrase | [
"Rewritten Question: \nA motel charges a flat fee for the first night plus a fixed amount per additional night. George pays $155 for 3 nights and Noah pays $290 for 6 nights. Find the flat fee.\n\nStep 1: Define variables.\nLet \\( F \\) be the flat fee for the first night.\nLet \\( D \\) be the daily rate for each... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Let triangle $ABC$ be a right triangle in the xy-plane with a right angle at $C$. Given that the length of the hypotenuse $AB$ is $60$, and that the medians through $A$ and $B$ lie along the lines $y=x+3$ and $y=2x+4$ respectively, find the area of triangle $ABC$.\n"
},
{
... | null | tiger_lab_math | 43,454 | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 400 | rephrase | [
"Rewritten Question: Triangle \\(ABC\\) is a right triangle with a right angle at \\(C\\), hypotenuse \\(AB = 60\\). Medians from \\(A\\) and \\(B\\) are on lines \\(y = x + 3\\) and \\(y = 2x + 4\\) respectively. Find the area of \\(\\triangle ABC\\).\n\nStep-by-step solution:\n1. Let \\(A = (x_1, y_1)\\) and \\(B... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
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"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "1. (2004 National College Entrance Examination Chongqing Paper) The solution set of the inequality $x+\\frac{2}{x+1}>2$ is\nA. $(-1,0) \\cup(1,+\\infty)$\nB. $(-\\cdots,-1) \\cup(0,1)$\nC. $(-1,0) \\cup(0,1)$\nD. $(-\\infty,-1) \\cup(1,+\\infty)$"
},
{
"from": "assistant"... | 1. (2004 National College Entrance Examination Chongqing Paper) The solution set of the inequality $x+\frac{2}{x+1}>2$ is
A. $(-1,0) \cup(1,+\infty)$
B. $(-\cdots,-1) \cup(0,1)$
C. $(-1,0) \cup(0,1)$
D. $(-\infty,-1) \cup(1,+\infty)$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | A | rephrase | [
"Rewritten Question: Solve the inequality \\( x + \\frac{2}{x+1} > 2 \\).\n\nStep 1: Rewrite the inequality.\n\\[ x + \\frac{2}{x+1} - 2 > 0 \\]\n\nStep 2: Combine terms over a common denominator.\n\\[ \\frac{x(x+1) + 2 - 2(x+1)}{x+1} > 0 \\]\n\\[ \\frac{x^2 + x + 2 - 2x - 2}{x+1} > 0 \\]\n\\[ \\frac{x^2 - x}{x+1} ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "## 29. Pretzels and Pretzelkins\n\n- Here's another problem,—began the Gryphon. One day, the Mock Turtle went to the store to buy pretzels for the next tea party.\n- How much are your pretzels?—he asked the store owner.\n- The price depends on the size: I can offer you small pret... | ## 29. Pretzels and Pretzelkins
- Here's another problem,—began the Gryphon. One day, the Mock Turtle went to the store to buy pretzels for the next tea party.
- How much are your pretzels?—he asked the store owner.
- The price depends on the size: I can offer you small pretzelkins and large pretzels. One pretzel cost... | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 6 | rephrase | [
"Rewritten Question: \nIf one pretzel costs as much as three pretzelkins, and seven pretzels and four pretzelkins cost twelve cents more than four pretzels and seven pretzelkins, how much does one pretzel cost?\n\nLet:\n- \\( p \\) be the cost of one pretzel in cents,\n- \\( k \\) be the cost of one pretzelkin in c... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
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"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Which of the following calculations is correct?\n\nA: $\\sqrt{12}=3\\sqrt{2}$\n\nB: $\\frac{\\sqrt{6}}{2}=\\sqrt{3}$\n\nC: $\\sqrt{3}+\\sqrt{2}=\\sqrt{5}$\n\nD: $(\\sqrt{3})^2=3$"
},
{
"from": "assistant",
"value": "<think>Okay, let's see. I need to figure out which o... | Which of the following calculations is correct?
A: $\sqrt{12}=3\sqrt{2}$
B: $\frac{\sqrt{6}}{2}=\sqrt{3}$
C: $\sqrt{3}+\sqrt{2}=\sqrt{5}$
D: $(\sqrt{3})^2=3$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | D | rephrase | [
"Rewritten Question: \n\nEvaluate which calculation is correct:\n\nA: $\\sqrt{12}=3\\sqrt{2}$\n\nB: $\\frac{\\sqrt{6}}{2}=\\sqrt{3}$\n\nC: $\\sqrt{3}+\\sqrt{2}=\\sqrt{5}$\n\nD: $(\\sqrt{3})^2=3$\n\nStep 1: Evaluate A.\n$\\sqrt{12} = \\sqrt{4*3} = 2\\sqrt{3} \\neq 3\\sqrt{2}$. So, A is incorrect.\n\nStep 2: Evaluate... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
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"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Given in the Cartesian coordinate system, there is a point $A(0,1)$, and vectors $\\overrightarrow{AB}=(-4,-3)$, $\\overrightarrow{BC}=(-7,-4)$. Then, the coordinates of point $C$ are $(\\quad)$.\nA: $(11,8)$\nB: $(3,2)$\nC: $(-11,-6)$\nD: $(-3,0)$"
},
{
"from": "assistan... | Given in the Cartesian coordinate system, there is a point $A(0,1)$, and vectors $\overrightarrow{AB}=(-4,-3)$, $\overrightarrow{BC}=(-7,-4)$. Then, the coordinates of point $C$ are $(\quad)$.
A: $(11,8)$
B: $(3,2)$
C: $(-11,-6)$
D: $(-3,0)$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | C | rephrase | [
"Rewritten Question: Given point $A(0,1)$, vector $\\overrightarrow{AB}=(-4,-3)$, and vector $\\overrightarrow{BC}=(-7,-4)$, find the coordinates of point $C$.\n\nStep 1: Find the coordinates of point $B$ using vector addition from point $A$.\n- The coordinates of point $B$ can be found by adding vector $\\overrigh... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "The monotonic decreasing interval of the function $f(x) = x^3 - 15x^2 - 33x + 6$ is ( )\n\nA: $(-11, 1)$\n\nB: $(-1, 11)$\n\nC: $(-\\infty, -1) \\cup (11, +\\infty)$\n\nD: $(-\\infty, -1)$ and $(11, +\\infty)$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I n... | The monotonic decreasing interval of the function $f(x) = x^3 - 15x^2 - 33x + 6$ is ( )
A: $(-11, 1)$
B: $(-1, 11)$
C: $(-\infty, -1) \cup (11, +\infty)$
D: $(-\infty, -1)$ and $(11, +\infty)$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | B | rephrase | [
"Rewritten Question: Find the monotonic decreasing interval of \\( f(x) = x^3 - 15x^2 - 33x + 6 \\).\n\nStep 1: Compute the first derivative of \\( f(x) \\).\n\\[ f'(x) = 3x^2 - 30x - 33 \\]\n\nStep 2: Set the first derivative equal to zero to find critical points.\n\\[ 3x^2 - 30x - 33 = 0 \\]\nDivide through by 3:... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given \\( x_{1}^{2} + x_{2}^{2} + \\cdots + x_{n}^{2} = 1 \\), prove that \\( a_{1} x_{1} + a_{2} x_{2} + \\cdots + a_{n} x_{n} \\leq \\sqrt{a_{1}^{2} + a_{2}^{2} + \\cdots + a_{n}^{2}} \\)."
},
{
"from": "assistant",
"valu... | Given \( x_{1}^{2} + x_{2}^{2} + \cdots + x_{n}^{2} = 1 \), prove that \( a_{1} x_{1} + a_{2} x_{2} + \cdots + a_{n} x_{n} \leq \sqrt{a_{1}^{2} + a_{2}^{2} + \cdots + a_{n}^{2}} \). | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | a_{1} x_{1} + a_{2} x_{2} + \cdots + a_{n} x_{n} \leq \sqrt{a_{1}^{2} + a_{2}^{2} + \cdots + a_{n}^{2}} | rephrase | [
"Rewritten Question: Prove that for any real numbers \\(x_1, x_2, \\ldots, x_n\\) such that \\(x_1^2 + x_2^2 + \\cdots + x_n^2 = 1\\), and for any real numbers \\(a_1, a_2, \\ldots, a_n\\), the inequality \\(a_1 x_1 + a_2 x_2 + \\cdots + a_n x_n \\leq \\sqrt{a_1^2 + a_2^2 + \\cdots + a_n^2}\\) holds.\n\nTo prove th... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "On the school playground, the relationship between the flagpole used for raising the flag and the ground is ( ).\n\nA: Parallel lines \nB: Line parallel to plane \nC: Perpendicular lines \nD: Line perpendicular to plane"
},
{
"from": "assistant",
"value": "<think>\... | On the school playground, the relationship between the flagpole used for raising the flag and the ground is ( ).
A: Parallel lines
B: Line parallel to plane
C: Perpendicular lines
D: Line perpendicular to plane | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | D | rephrase | [
"Rewritten Question: What is the geometric relationship between a flagpole standing upright on the ground and the ground itself?\n\nStep 1: Understand that a flagpole standing upright means it forms a right angle with the ground.\nStep 2: Recall the definition of perpendicular lines - two lines are perpendicular if... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
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