conversations listlengths 2 2 | question stringlengths 33 1.27k | source null | id null | prompt listlengths 2 2 | answer stringclasses 492
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
value | task_config stringclasses 1
value | model_responses__example_annotation listlengths 1 1 | model_responses__example_annotation__eval_is_correct listlengths 1 1 | model_responses__example_annotation__eval_extracted_answers listlengths 1 1 | prompt_type stringclasses 2
values | reflection_prompt listlengths 2 2 | model_responses__mutated_prompts_reflection listlengths 1 1 | model_responses__mutated_prompts_reflection__finish_reason_length_flags listlengths 1 1 | model_responses__mutated_prompts_reflection__length_partial_responses listlengths 1 1 | reflection_prompt__mutated_prompts_reflection__metadata dict | model_responses__mutated_prompts_reflection__metadata dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "## Task B-4.2.\n\nDetermine the smallest natural number $m$ for which the product $3^{\\frac{1}{55}} \\cdot 3^{\\frac{4}{55}} \\cdot 3^{\\frac{7}{55}} \\cdot \\ldots \\cdot 3^{\\frac{3 m-2}{55}}$ is greater than 729?"
},
{
"from": "assistant",
"value": "<think>\nOkay,... | ## Task B-4.2.
Determine the smallest natural number $m$ for which the product $3^{\frac{1}{55}} \cdot 3^{\frac{4}{55}} \cdot 3^{\frac{7}{55}} \cdot \ldots \cdot 3^{\frac{3 m-2}{55}}$ is greater than 729? | 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... | 16 | {
"api_url": "http://10.32.36.232:9080/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... | openthoughts | openthoughts | [
"First, let's simplify the expression given:\n\\[3^{\\frac{1}{55}} \\cdot 3^{\\frac{4}{55}} \\cdot 3^{\\frac{7}{55}} \\cdot \\ldots \\cdot 3^{\\frac{3 m-2}{55}}\\]\n\nUsing properties of exponents, we can combine the terms into one exponent:\n\\[3^{(\\frac{1+4+7+\\ldots+(3m-2)}{55})}\\]\n\nThe sequence inside the e... | [
true
] | [
"16"
] | alternative_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly identified the steps required to solve the problem and followed through with the necessary calculations. It derived the correct quadratic inequality and solved it accurately, arriving at the conclusion that the smallest natural number \\( m \\) is 16. This aligns with... | [
false
] | [
""
] | {
"api_url": "http://10.32.37.4:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm/Q... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "## Task B-4.2.\n\nDetermine the smallest natural number $m$ for which the product $3^{\\frac{1}{55}} \\cdot 3^{\\frac{4}{55}} \\cdot 3^{\\frac{7}{55}} \\cdot \\ldots \\cdot 3^{\\frac{3 m-2}{55}}$ is greater than 729?"
},
{
"from": "assistant",
"value": "<think>\nOkay,... | ## Task B-4.2.
Determine the smallest natural number $m$ for which the product $3^{\frac{1}{55}} \cdot 3^{\frac{4}{55}} \cdot 3^{\frac{7}{55}} \cdot \ldots \cdot 3^{\frac{3 m-2}{55}}$ is greater than 729? | 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... | 16 | {
"api_url": "http://10.32.36.232:9080/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... | openthoughts | openthoughts | [
"First, let's simplify the given expression. The expression is \\(3^{\\frac{1}{55}} \\cdot 3^{\\frac{4}{55}} \\cdot 3^{\\frac{7}{55}} \\cdot \\ldots \\cdot 3^{\\frac{3m-2}{55}}\\). Using the property of exponents that states \\(a^x \\cdot a^y = a^{x+y}\\), we can combine the exponents:\n\n\\[3^{\\left(\\frac{1}{55}... | [
true
] | [
"16"
] | alternative_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly identified the steps to solve the problem, including combining the exponents into a single power of 3, finding the sum of the arithmetic sequence, and setting up the inequality. The quadratic solution and checking the values for \\(m=15\\) and \\(m=16\\) were also don... | [
false
] | [
""
] | {
"api_url": "http://10.32.37.4:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm/Q... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \(...TRUNCATED) | "$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \\\\\nP_{\\mathrm{u}}=\\f(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: \nGiven \\( T_n = 1 + 2 + 3 + \\cdots + n \\), find the value of \\( P_{1091} (...TRUNCATED) | [
false
] | [
"(B) 2.3"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking the steps and logic used in the model response:\n\nThe model(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \(...TRUNCATED) | "$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \\\\\nP_{\\mathrm{u}}=\\f(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: \nIf \\( T_n = 1 + 2 + 3 + \\cdots + n \\), find \\( P_{1091} \\) where \\( P_(...TRUNCATED) | [
true
] | [
"D"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model response correctly identified the definition of \\( T_n \\) a(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \(...TRUNCATED) | "$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \\\\\nP_{\\mathrm{u}}=\\f(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve for \\( P_{1091} \\), we first need to understand the expression for \\( T_n \\). The sum(...TRUNCATED) | [
true
] | [
"D"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly derived the formula for \\( P_n \\) as \\( \\frac{3(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \(...TRUNCATED) | "$$\n\\begin{array}{l}\n\\text { 25. If } T_{\\mathrm{n}}=1+2+3+\\cdots+n, \\\\\nP_{\\mathrm{u}}=\\f(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["First, let's understand what \\( T_n \\) represents. It is the sum of the first \\( n \\) natural (...TRUNCATED) | [
true
] | [
"D"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly identified the nature of \\( T_n \\) and d(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\f(...TRUNCATED) | "## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\frac{\\arccos ^{3} x-1}{\(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \arccos x - \frac{\arccos^4 x}{4} + C | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Calculate the indefinite integral:\n$$\n\\int \\frac{\\arccos ^{3} x-1}{\\sqrt(...TRUNCATED) | [
true
] | [
"\\arccos x - \\frac{\\arccos^4 x}{4} + C"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly identified the substitution \\( u = \\arccos(x) \\)(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\f(...TRUNCATED) | "## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\frac{\\arccos ^{3} x-1}{\(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \arccos x - \frac{\arccos^4 x}{4} + C | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Calculate the indefinite integral:\n$$\n\\int \\frac{\\arccos ^{3} x-1}{\\sqrt(...TRUNCATED) | [
true
] | [
"\\arccos x - \\frac{\\arccos^4 x}{4} + C"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking the differentiation of the proposed solution. The proposed s(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\f(...TRUNCATED) | "## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\frac{\\arccos ^{3} x-1}{\(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \arccos x - \frac{\arccos^4 x}{4} + C | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve the integral \n\n\\[\n\\int \\frac{\\arccos^3 x - 1}{\\sqrt{1-x^2}} \\, dx,\n\\]\n\nwe st(...TRUNCATED) | [
true
] | [
"\\arccos x - \\frac{\\arccos^4 x}{4} + C"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response starts off correctly by suggesting a substitution \\(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\f(...TRUNCATED) | "## Problem Statement\n\nCalculate the indefinite integral:\n\n$$\n\\int \\frac{\\arccos ^{3} x-1}{\(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \arccos x - \frac{\arccos^4 x}{4} + C | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve the given integral:\n\\[ \\int \\frac{\\arccos^3 x - 1}{\\sqrt{1-x^2}} \\, dx \\]\n\n**St(...TRUNCATED) | [
false
] | [
"\\arccos x - \\frac{(\\arccos x)^4}{4} + C"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly identifies the integral solution through s(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.37.4:9080/v1","backend":"litellm","chat_template_applied":true,"generation_(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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