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The dataset generation failed
Error code:   DatasetGenerationError
Exception:    CastError
Message:      Couldn't cast
n_questions: int64
empirical_accuracy: double
pass_at_k: struct<pass@1: double, pass@2: double, pass@4: double, pass@8: double, pass@16: double, pass@32: dou (... 4 chars omitted)
  child 0, pass@1: double
  child 1, pass@2: double
  child 2, pass@4: double
  child 3, pass@8: double
  child 4, pass@16: double
  child 5, pass@32: double
gt: string
completions: list<item: string>
  child 0, item: string
question_index: int64
question: string
to
{'question_index': Value('int64'), 'question': Value('string'), 'gt': Value('string'), 'completions': List(Value('string'))}
because column names don't match
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1827, in _prepare_split_single
                  for key, table in generator:
                                    ^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
                  for item in generator(*args, **kwargs):
                              ~~~~~~~~~^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
                  self._cast_table(pa_table, json_field_paths=json_field_paths),
                  ~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
                  pa_table = table_cast(pa_table, self.info.features.arrow_schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2306, in cast_table_to_schema
                  raise CastError(
                  ...<3 lines>...
                  )
              datasets.table.CastError: Couldn't cast
              n_questions: int64
              empirical_accuracy: double
              pass_at_k: struct<pass@1: double, pass@2: double, pass@4: double, pass@8: double, pass@16: double, pass@32: dou (... 4 chars omitted)
                child 0, pass@1: double
                child 1, pass@2: double
                child 2, pass@4: double
                child 3, pass@8: double
                child 4, pass@16: double
                child 5, pass@32: double
              gt: string
              completions: list<item: string>
                child 0, item: string
              question_index: int64
              question: string
              to
              {'question_index': Value('int64'), 'question': Value('string'), 'gt': Value('string'), 'completions': List(Value('string'))}
              because column names don't match
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
                  parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
                                                                        ~~~~~~~~~~~~~~~~~~~~~~~~~^
                      builder, max_dataset_size_bytes=max_dataset_size_bytes
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                  )
                  ^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
                  builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
                  ~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1694, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ~~~~~~~~~~~~~~~~~~~~~~~~~~^
                      gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                  ):
                  ^
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1880, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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question_index
int64
question
string
gt
string
completions
list
0
Convert the point $(0,3)$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$
We have that $r = \sqrt{0^2 + 3^2} = 3.$ Also, if we draw the line connecting the origin and $(0,3),$ this line makes an angle of $\frac{\pi}{2}$ with the positive $x$-axis. [asy] unitsize(0.8 cm); draw((-0.5,0)--(3.5,0)); draw((0,-0.5)--(0,3.5)); draw(arc((0,0),3,0,90),red,Arrow(6)); dot((0,3), red); label("$(0,3)...
[ "To convert the point $(0,3)$ from rectangular coordinates to polar coordinates, we need to find the radius $r$ and the angle $\\theta$.\n\nFirst, let's find the radius $r$. The radius is the distance from the origin to the point. Since the point is on the y-axis, its distance from the origin is simply the absolute...
1
Define \[p = \sum_{k = 1}^\infty \frac{1}{k^2} \quad \text{and} \quad q = \sum_{k = 1}^\infty \frac{1}{k^3}.\]Find a way to write \[\sum_{j = 1}^\infty \sum_{k = 1}^\infty \frac{1}{(j + k)^3}\]in terms of $p$ and $q.$
We count the number of times $\frac{1}{n^3}$ appears in the sum \[\sum_{j = 1}^\infty \sum_{k = 1}^\infty \frac{1}{(j + k)^3},\]where $n$ is a fixed positive integer. (In other words, we are conditioning the sum on $j + k$.) We get a term of $\frac{1}{n^3}$ each time $j + k = n.$ The pairs $(j,k)$ that work are $(1,...
[ "To find a way to write the given double sum in terms of $p$ and $q$, let's start by examining the structure of the double sum.\n\n\\[\\sum_{j = 1}^\\infty \\sum_{k = 1}^\\infty \\frac{1}{(j + k)^3}\\]\n\nNotice that each term in the sum involves the sum of two fractions, each with a denominator that is a cube of a...
2
If $f(x) = \frac{3x-2}{x-2}$, what is the value of $f(-2) +f(-1)+f(0)$? Express your answer as a common fraction.
$f(-2)+f(-1)+f(0)=\frac{3(-2)-2}{-2-2}+\frac{3(-1)-2}{-1-2}+\frac{3(0)-2}{0-2}=\frac{-8}{-4}+\frac{-5}{-3}+\frac{-2}{-2}=2+\frac{5}{3}+1=\boxed{\frac{14}{3}}$
[ "To find the value of $f(-2) + f(-1) + f(0)$, I'll start by evaluating each function at the given points.\n\nFirst, I'll calculate $f(-2)$:\n\\[ f(-2) = \\frac{3(-2) - 2}{-2 - 2} = \\frac{-6 - 2}{-4} = \\frac{-8}{-4} = 2 \\]\n\nNext, I'll calculate $f(-1)$:\n\\[ f(-1) = \\frac{3(-1) - 2}{-1 - 2} = \\frac{-3 - 2}{-3...
3
How many positive whole-number divisors does 196 have?
First prime factorize $196=2^2\cdot7^2$. The prime factorization of any divisor of 196 cannot include any primes other than 2 and 7. We are free to choose either 0, 1, or 2 as the exponent of 2 in the prime factorization of a divisor of 196. Similarly, we may choose 0, 1, or 2 as the exponent of 7. In total, there ...
[ "To determine the number of positive whole-number divisors of 196, I'll start by finding its prime factorization.\n\nFirst, I'll break down 196 into its prime factors:\n196 = 2^2 * 7^2\n\nNext, I'll use the formula for finding the total number of divisors based on the prime factorization:\nFor a number in the form ...
4
"The results of a cross-country team's training run are graphed below. Which student has the greates(...TRUNCATED)
"Evelyn covered more distance in less time than Briana, Debra and Angela, so her average speed is gr(...TRUNCATED)
["To determine which student has the greatest average speed, we need to calculate the average speed (...TRUNCATED)
5
"A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the tri(...TRUNCATED)
"The side length of the hexagon is equal to the side length of one of the equilateral triangles. Si(...TRUNCATED)
["To determine the perimeter of the regular hexagon, I'll start by understanding the relationship be(...TRUNCATED)
6
"What is the smallest positive perfect cube that can be written as the sum of three consecutive inte(...TRUNCATED)
"The sum of three consecutive integers takes the form $(k-1)+(k)+(k+1)=3k$ and hence is a multiple o(...TRUNCATED)
["To find the smallest positive perfect cube that can be written as the sum of three consecutive int(...TRUNCATED)
7
"The set of points $(x,y,z)$ that satisfy\n\\[2x = 3y = -z\\]is a line.\n\nThe set of points $(x,y,z(...TRUNCATED)
"For the first line, let $t = 2x = 3y = -z.$ Then\n\\[\\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatri(...TRUNCATED)
["To find the angle between the two lines, we first need to determine the direction vectors of each (...TRUNCATED)
8
"What is the distance, in units, between the points $(2, -6)$ and $(-4, 3)$? Express your answer in (...TRUNCATED)
"We use the distance formula: \\begin{align*}\n\\sqrt{(2 - (-4))^2 + ((-6) - 3)^2} &= \\sqrt{6^2 + (...TRUNCATED)
["To find the distance between the two points, I'll use the distance formula:\n\n\\[d = \\sqrt{(x_2 (...TRUNCATED)
9
"The expression $2\\cdot 3 \\cdot 4\\cdot 5+1$ is equal to 121, since multiplication is carried out (...TRUNCATED)
"By the associative property of multiplication, it doesn't help to insert parentheses that specify t(...TRUNCATED)
["To determine the number of values that can be obtained from the expression $2\\cdot 3\\cdot 4 \\cd(...TRUNCATED)
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