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_rationalized | [
"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\\) using the formula for the \\(n\\)-th term of a geometric sequence, which is \\(a_n = a_1 q^{n-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": "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_rationalized | [
"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,
"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": "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_rationalized | [
"Rewritten Question: A motel charges a flat fee for the first night and a fixed amount for each additional night. George stays for 3 nights paying $155, and Noah stays for 6 nights paying $290. Find the flat fee for the first night.\n\nLet's denote:\n- \\( F \\) as the flat fee for the first night.\n- \\( D \\) as ... | [
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_rationalized | [
"Rewritten Question: Let triangle \\(ABC\\) be a right triangle in the xy-plane with a right angle at \\(C\\). The length of the hypotenuse \\(AB\\) is 60, and 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\nStep ... | [
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": "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_rationalized | [
"Rewritten Question: Solve the inequality \\( x + \\frac{2}{x+1} > 2 \\).\n\nStep 1: Move all terms to one side of the inequality.\n\\[ x + \\frac{2}{x+1} - 2 > 0 \\]\n\nStep 2: Combine like 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 \\]... | [
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_rationalized | [
"Rewritten Question: \nOne pretzel costs as much as three pretzelkins. Seven pretzels and four pretzelkins cost twelve cents more than four pretzels and seven pretzelkins. Find the cost of one pretzel.\n\nStep 1: Define variables:\nLet \\( p \\) be the cost of one pretzel.\nLet \\( k \\) be the cost of one pretzelk... | [
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": "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_rationalized | [
"Rewritten Question: 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: $(\\sqrt{3})^2=3$\n\nStep 1: Evaluate option A.\n$\\sqrt{12} = \\sqrt{4 \\cdot 3} = 2\\sqrt{3}$. Therefore, $A$ is incorrect because $... | [
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": "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_rationalized | [
"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: Determine the coordinates of point \\( B \\).\n- The coordinates of \\( B \\) can be found by adding vector \\( \\ove... | [
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_rationalized | [
"Rewritten Question: Find the monotonic decreasing interval of the function \\( f(x) = x^3 - 15x^2 - 33x + 6 \\).\n\nTo find the monotonic decreasing intervals of the function, we need to determine where its derivative is negative. Let's start by finding the first derivative of the function:\n\n\\[ f'(x) = 3x^2 - 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_rationalized | [
"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\\), the expression \\(a_1 x_1 + a_2 x_2 + \\cdots + a_n x_n\\) is bounded above by \\(\\sqrt{a_1^2 + a_2^2 + \\cdots + a_n^2}\\).\n\nTo prove this, we can use the Cauchy-Schwarz inequal... | [
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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