conversations listlengths 2 2 | question stringlengths 30 2.21k | source null | id null | prompt listlengths 2 2 | answer stringclasses 481
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": "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{9}=1$, respectively, and the chord $DE$ of the ellipse passes through the focus $F_{1}$, then the perimeter of $\\triangle DEF_{2}$ is ( ).\n\nA: $64$\n\nB: $20$\n\nC: $16$\n\nD: $3... | Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, respectively, and the chord $DE$ of the ellipse passes through the focus $F_{1}$, then the perimeter of $\triangle DEF_{2}$ is ( ).
A: $64$
B: $20$
C: $16$
D: $36$ | 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 | {
"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... | openthoughts | openthoughts | [
"Rewritten Question: Given the ellipse $\\frac{x^2}{16} + \\frac{y^2}{9} = 1$ and its foci $F_1$ and $F_2$, if a chord $DE$ passes through $F_1$, find the perimeter of $\\triangle DEF_2$.\n\nStep 1: Identify key properties of the ellipse.\n- The equation $\\frac{x^2}{16} + \\frac{y^2}{9} = 1$ shows that the semi-ma... | [
false
] | [
"(16)"
] | rephrase_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 properties of the ellipse and used the fact that the sum of distances from any point on the ellipse to the two foci is constant and equal to 2a, which is 8 in this case. It also correctly deduced that since the chord DE passes through F1, the perimeter ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/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... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{9}=1$, respectively, and the chord $DE$ of the ellipse passes through the focus $F_{1}$, then the perimeter of $\\triangle DEF_{2}$ is ( ).\n\nA: $64$\n\nB: $20$\n\nC: $16$\n\nD: $3... | Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, respectively, and the chord $DE$ of the ellipse passes through the focus $F_{1}$, then the perimeter of $\triangle DEF_{2}$ is ( ).
A: $64$
B: $20$
C: $16$
D: $36$ | 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 | {
"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... | openthoughts | openthoughts | [
"Rewritten Question: Given the ellipse \\(\\frac{x^2}{16} + \\frac{y^2}{9} = 1\\), find the perimeter of \\(\\triangle DEF_2\\) where \\(DE\\) is a chord passing through the left focus \\(F_1\\) and \\(F_2\\) is the right focus.\n\nStep 1: Identify the key elements of the ellipse.\n- The equation of the ellipse is ... | [
false
] | [
"(C)"
] | rephrase_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 properties of the ellipse and used the fact that the sum of distances from any point on the ellipse to the two foci is constant and equal to the length of the major axis, which is 8. It also correctly reasoned that since the chord DE passes through one ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/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... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{9}=1$, respectively, and the chord $DE$ of the ellipse passes through the focus $F_{1}$, then the perimeter of $\\triangle DEF_{2}$ is ( ).\n\nA: $64$\n\nB: $20$\n\nC: $16$\n\nD: $3... | Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, respectively, and the chord $DE$ of the ellipse passes through the focus $F_{1}$, then the perimeter of $\triangle DEF_{2}$ is ( ).
A: $64$
B: $20$
C: $16$
D: $36$ | 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 | {
"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... | openthoughts | openthoughts | [
"Rewritten Question: Given the ellipse \\(\\frac{x^2}{16} + \\frac{y^2}{9} = 1\\), if a chord \\(DE\\) passes through the left focus \\(F_1\\), find the perimeter of \\(\\triangle DEF_2\\).\n\nStep 1: Identify key properties of the ellipse.\nThe equation \\(\\frac{x^2}{16} + \\frac{y^2}{9} = 1\\) indicates that the... | [
false
] | [
"(16)"
] | rephrase_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 properties of the ellipse and used the definition of an ellipse to conclude that the perimeter of \\(\\triangle DEF_2\\) is 16. The steps taken are logical and consistent with the properties of ellipses. No errors were found in the reasoning or calculat... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/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... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\fr(...TRUNCATED) | "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | C | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Given the ellipse \\(\\frac{x^2}{16} + \\frac{y^2}{9} = 1\\) with foci \\(F_1\(...TRUNCATED) | [
false
] | [
"(16)"
] | 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 identifies the key properties of the ellipse and us(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\fr(...TRUNCATED) | "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | C | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve the problem, we need to understand the properties of ellipses and how chords passing thro(...TRUNCATED) | [
false
] | [
"(16)"
] | 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 identifies the key properties of the ellipse and us(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\fr(...TRUNCATED) | "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | C | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve this problem, let's first understand the properties of the given ellipse and the triangle(...TRUNCATED) | [
false
] | [
"16"
] | 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 identified the key properties of the ellipse and us(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\fr(...TRUNCATED) | "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | C | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Firstly, let's identify key properties of the ellipse given by \\(\\frac{x^2}{16} + \\frac{y^2}{9}(...TRUNCATED) | [
false
] | [
"16"
] | 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 identified the semi-major axis \\(a = 4\\) and the (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\fr(...TRUNCATED) | "Given that $F_{1}$ and $F$ are the left and right foci of the ellipse $\\frac{x^2}{16}+\\frac{y^2}{(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | C | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve the problem, we need to understand the properties of ellipses and how chords passing thro(...TRUNCATED) | [
true
] | [
"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 correctly identified the semi-major axis \\(a = 4\\) and calc(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Return your final response within \\boxed{}. The recurring decimal \\(0 . \(...TRUNCATED) | "The recurring decimal \\(0 . \\dot{x} y \\dot{z}\\), where \\(x, y, z\\) denote digits between 0 an(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 660 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: A repeating decimal of the form \\(0.\\overline{xyz}\\) (where \\(x\\), \\(y\\(...TRUNCATED) | [
true
] | [
"660"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | [
""
] | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Return your final response within \\boxed{}. The recurring decimal \\(0 . \(...TRUNCATED) | "The recurring decimal \\(0 . \\dot{x} y \\dot{z}\\), where \\(x, y, z\\) denote digits between 0 an(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 660 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: A repeating decimal of the form \\(0.\\overline{xyz}\\) is expressed as a frac(...TRUNCATED) | [
true
] | [
"660"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | [
""
] | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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