conversations listlengths 2 2 | question stringlengths 12 5.4k ⌀ | source stringclasses 8
values | id int64 21 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 560 ⌀ | prompt_type stringclasses 1
value | 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": "Given the line $ax+y+1=0$ always passes through a fixed point, the coordinates of this fixed point are \\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that the line ax + y + 1 = 0 always passes through a fixed point,... | Given the line $ax+y+1=0$ always passes through a fixed point, the coordinates of this fixed point are \_\_\_\_\_\_. | 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... | (0, -1) | rephrase | [
"Rewritten Question: Find the coordinates of the fixed point through which the line \\( ax + y + 1 = 0 \\) always passes.\n\nTo find the fixed point that the line \\( ax + y + 1 = 0 \\) always passes through regardless of the value of \\( a \\), we need to identify a point \\((x_0, y_0)\\) such that substituting 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": "Given $x\\_1=\\log \\_{\\frac {1}{3}}2$, $x\\_2=2^{-\\frac {1}{2}}$, and $(\\frac {1}{3})^{x3}=\\log \\_{3}x\\_{3}$, determine the correct relationship among $x\\_1$, $x\\_2$, and $x\\_3$.\n\nA: $x\\_1 < x\\_3 < x\\_2$\nB: $x\\_2 < x\\_1 < x\\_3$\nC: $x\\_1 < x\\_2 < x\\_3$\nD: $... | Given $x\_1=\log \_{\frac {1}{3}}2$, $x\_2=2^{-\frac {1}{2}}$, and $(\frac {1}{3})^{x3}=\log \_{3}x\_{3}$, determine the correct relationship among $x\_1$, $x\_2$, and $x\_3$.
A: $x\_1 < x\_3 < x\_2$
B: $x\_2 < x\_1 < x\_3$
C: $x\_1 < x\_2 < x\_3$
D: $x\_3 < x\_1 < x\_2$ | 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... | C | rephrase | [
"Rewritten Question: Determine the correct order of \\(x_1 = \\log_{\\frac{1}{3}} 2\\), \\(x_2 = 2^{-\\frac{1}{2}}\\), and \\(x_3\\) where \\(\\left(\\frac{1}{3}\\right)^{x_3} = \\log_3 x_3\\).\n\nStep 1: Evaluate \\(x_1 = \\log_{\\frac{1}{3}} 2\\).\nSince \\(\\log_{\\frac{1}{3}} 2 = -\\log_3 2\\), we know that \\(... | [
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. Given sets\n$$\n\\begin{array}{l}\nS_{1}=\\left\\{(x, y) \\mid \\lg \\left(1+x^{2}+y^{2}\\right) \\leqslant 1+\\lg (x+y)\\right\\}, \\\\\nS_{2}=\\left\\{(x, y) \\mid \\lg \\left(2+x^{2}+y^{2}\\right) \\leqslant 2+\\lg (x+y)\\right\\} .\n\\end{array}\n$$\n\nThen the ratio of th... | 1. Given sets
$$
\begin{array}{l}
S_{1}=\left\{(x, y) \mid \lg \left(1+x^{2}+y^{2}\right) \leqslant 1+\lg (x+y)\right\}, \\
S_{2}=\left\{(x, y) \mid \lg \left(2+x^{2}+y^{2}\right) \leqslant 2+\lg (x+y)\right\} .
\end{array}
$$
Then the ratio of the area of $S_{2}$ to the area of $S_{1}$ is ( ).
(A) 99
(B) 100
(C) 101
... | 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: \nFind the ratio of the areas of the regions defined by:\n\\[ S_1 = \\left\\{(x, y) \\mid \\lg \\left(1 + x^2 + y^2\\right) \\leq 1 + \\lg (x + y)\\right\\} \\]\n\\[ S_2 = \\left\\{(x, y) \\mid \\lg \\left(2 + x^2 + y^2\\right) \\leq 2 + \\lg (x + y)\\right\\} \\]\n\nStep-by-step solution:\n\n1... | [
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 that function $f(x)$ is an even function defined on $\\mathbb{R}$ and is monotonically increasing in the interval $[0,+\\infty)$. If the real number $a$ satisfies $f(\\log_{2}a)+f(\\log_{\\frac{1}{2}}a) < 2f(1)$, determine the range of $a$.\n\nA: $[1,2]$\nB: $(0, \\frac{1}{... | Given that function $f(x)$ is an even function defined on $\mathbb{R}$ and is monotonically increasing in the interval $[0,+\infty)$. If the real number $a$ satisfies $f(\log_{2}a)+f(\log_{\frac{1}{2}}a) < 2f(1)$, determine the range of $a$.
A: $[1,2]$
B: $(0, \frac{1}{2}]$
C: $(\frac{1}{2},2)$
D: $(0,2]$ | 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... | C | rephrase | [
"Rewritten Question: Given $f(x)$ is an even function and monotonically increasing on $[0, +\\infty)$, if $a$ satisfies $f(\\log_{2}a)+f(\\log_{\\frac{1}{2}}a) < 2f(1)$, find the range of $a$.\n\nStep 1: Simplify the logarithmic expressions.\nSince $\\log_{\\frac{1}{2}}a = -\\log_{2}a$, we can rewrite the inequalit... | [
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 organizing committee of the sports meeting needs to select four volunteers from Xiao Zhang, Xiao Zhao, Xiao Li, Xiao Luo, and Xiao Wang to take on four different tasks: translation, tour guide, etiquette, and driver. If Xiao Zhang and Xiao Zhao can only take on the first two ... | The organizing committee of the sports meeting needs to select four volunteers from Xiao Zhang, Xiao Zhao, Xiao Li, Xiao Luo, and Xiao Wang to take on four different tasks: translation, tour guide, etiquette, and driver. If Xiao Zhang and Xiao Zhao can only take on the first two tasks, while the other three can take on... | 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... | 36 | rephrase | [
"Rewritten Question: \nXiao Zhang and Xiao Zhao can only do 2 tasks each, while Xiao Li, Xiao Luo, and Xiao Wang can do any of the 4 tasks. Find the number of ways to assign 4 specific tasks (translation, tour guide, etiquette, driver) to 4 out of 5 people.\n\nStep 1: Identify who can do which tasks.\n- Xiao Zhang ... | [
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 that point $Q(a-1,a+2)$ lies on the $x$-axis, what are the coordinates of point $Q$?\n\nA: $(-3,0)$\n\nB: $(3,0)$\n\nC: $(0,3)$\n\nD: $(0,-3)$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is about finding the coordinates of point Q,... | Given that point $Q(a-1,a+2)$ lies on the $x$-axis, what are the coordinates of point $Q$?
A: $(-3,0)$
B: $(3,0)$
C: $(0,3)$
D: $(0,-3)$ | 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... | A | rephrase | [
"Rewritten Question: If a point Q has coordinates $(a-1, a+2)$ and lies on the x-axis, what are its coordinates?\n\nStep 1: Since the point lies on the x-axis, its y-coordinate must be zero.\nStep 2: Set the y-coordinate equal to zero: $a + 2 = 0$.\nStep 3: Solve for $a$: $a = -2$.\nStep 4: Substitute $a = -2$ into... | [
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": "## Task B-2.3.\n\nCalculate:\n\n$$\n\\frac{\\left(1+\\frac{1}{3}\\right)\\left(1+\\frac{1}{5}\\right) \\cdot \\ldots \\cdot\\left(1+\\frac{1}{2 n+1}\\right) \\cdot \\ldots \\cdot\\left(1+\\frac{1}{4047}\\right)}{\\sqrt{\\left(1-\\frac{1}{3^{2}}\\right)\\left(1-\\frac{1}{5^{2}}\\r... | ## Task B-2.3.
Calculate:
$$
\frac{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right) \cdot \ldots \cdot\left(1+\frac{1}{2 n+1}\right) \cdot \ldots \cdot\left(1+\frac{1}{4047}\right)}{\sqrt{\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{5^{2}}\right) \cdot \ldots \cdot\left(1-\frac{1}{(2 n+1)^{2}}\right) \cdot \ldo... | 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... | \sqrt{2024} | rephrase | [
"Rewritten Question: Calculate:\n\n$$\n\\frac{\\left(1+\\frac{1}{3}\\right)\\left(1+\\frac{1}{5}\\right) \\cdots \\left(1+\\frac{1}{4047}\\right)}{\\sqrt{\\left(1-\\frac{1}{3^2}\\right)\\left(1-\\frac{1}{5^2}\\right) \\cdots \\left(1-\\frac{1}{4047^2}\\right)}}\n$$\n\nStep 1: Simplify each term in the numerator.\nE... | [
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": "Solve the following system of equations:\n\n$$\n\\begin{gathered}\n\\frac{10}{2 x+3 y-29}+\\frac{9}{7 x-8 y+24}=8 \\\\\n\\frac{2 x+3 y-29}{2}=\\frac{7 x-8 y}{3}+8\n\\end{gathered}\n$$"
},
{
"from": "assistant",
"value": "<think>\nAlright, so I need to solve this syste... | Solve the following system of equations:
$$
\begin{gathered}
\frac{10}{2 x+3 y-29}+\frac{9}{7 x-8 y+24}=8 \\
\frac{2 x+3 y-29}{2}=\frac{7 x-8 y}{3}+8
\end{gathered}
$$ | 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... | (5, 7) | rephrase | [
"Rewritten Question: Solve the following system of equations:\n\\[\n\\begin{cases}\n\\frac{10}{2x + 3y - 29} + \\frac{9}{7x - 8y + 24} = 8 \\\\\n\\frac{2x + 3y - 29}{2} = \\frac{7x - 8y}{3} + 8\n\\end{cases}\n\\]\n\nStep-by-step solution:\n\nFirst, let's simplify the second equation:\n\\[ \\frac{2x + 3y - 29}{2} = ... | [
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 length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 80 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ? Please respond by ... | 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... | 159.2\% | rephrase | [
"Rewritten Question: \nIf the side of square A is doubled to form square B, and then the side of square B is increased by 80% to form square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?\n\nStep 1: Let's denote the side length of square A as \\( s \\).\n- The area ... | [
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 the function $f(2^x)$ has a domain of $[1, 2]$, find the domain of $f(\\log_2 x)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that the function f(2^x) has a domain of [1, 2], and we need to find the domain of f(log₂ x). Hmm, ... | Given the function $f(2^x)$ has a domain of $[1, 2]$, find the domain of $f(\log_2 x)$. | 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... | [4, 16] | rephrase | [
"Rewritten Question: Given the domain of \\( f(2^x) \\) is \\([1, 2]\\), find the domain of \\( f(\\log_2 x) \\).\n\nStep 1: Determine the range of values that \\( 2^x \\) takes when \\( x \\) is in \\([1, 2]\\).\n- When \\( x = 1 \\), \\( 2^x = 2^1 = 2 \\).\n- When \\( x = 2 \\), \\( 2^x = 2^2 = 4 \\).\nSo, the ra... | [
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 that the functions $f(x)$ and $g(x)$ defined on $\\mathbb{R}$ satisfy $\\frac{f(x)}{g(x)} = b^x$, and $f'(x)g(x) < f(x)g'(x)$, $\\frac{f(1)}{g(1)} + \\frac{f(-1)}{g(-1)} = \\frac{5}{2}$. If $\\{a_n\\}$ is a positive geometric sequence and $a_5a_7 + 2a_6a_8 + a_4a_{12} = \\f... | Given that the functions $f(x)$ and $g(x)$ defined on $\mathbb{R}$ satisfy $\frac{f(x)}{g(x)} = b^x$, and $f'(x)g(x) < f(x)g'(x)$, $\frac{f(1)}{g(1)} + \frac{f(-1)}{g(-1)} = \frac{5}{2}$. If $\{a_n\}$ is a positive geometric sequence and $a_5a_7 + 2a_6a_8 + a_4a_{12} = \frac{f(4)}{g(4)}$, find the value of $a_6 + a_8$. | 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... | \dfrac{1}{4} | rephrase | [
"Rewritten Question: Given $\\frac{f(x)}{g(x)} = b^x$, $f'(x)g(x) < f(x)g'(x)$, and $\\frac{f(1)}{g(1)} + \\frac{f(-1)}{g(-1)} = \\frac{5}{2}$, if $\\{a_n\\}$ is a positive geometric sequence and $a_5a_7 + 2a_6a_8 + a_4a_{12} = \\frac{f(4)}{g(4)}$, find $a_6 + a_8$.\n\nStep-by-step solution:\n1. From $\\frac{f(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": "Example 5 Let $a, b, c$ be the lengths of the sides of a right triangle, and $a \\leqslant b < c$. Find the maximum constant $k$, such that $a^{2}(b+c)+b^{2}(c+a)+c^{2}(a+b) \\geqslant k a b c$ holds for all right triangles, and determine when equality occurs."
},
{
"from... | Example 5 Let $a, b, c$ be the lengths of the sides of a right triangle, and $a \leqslant b < c$. Find the maximum constant $k$, such that $a^{2}(b+c)+b^{2}(c+a)+c^{2}(a+b) \geqslant k a b c$ holds for all right triangles, and determine when equality occurs. | 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... | 3\sqrt{2} + 2 | rephrase | [
"Rewritten Question: Given a right triangle with sides \\(a \\leqslant b < c\\), find the maximum constant \\(k\\) such that \\(a^2(b+c) + b^2(c+a) + c^2(a+b) \\geqslant kabc\\) holds, and determine when equality occurs.\n\nStep 1: Recognize that since \\(a, b, c\\) are the sides of a right triangle with \\(a \\leq... | [
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
} |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4