type stringclasses 4
values | q stringlengths 3 74 | a stringlengths 1 144 |
|---|---|---|
Derivatives | 7 \sqrt{x} + 10 | \frac{7}{2 \sqrt{x}} |
Derivatives | 7 \sqrt{x} - 2 | \frac{7}{2 \sqrt{x}} |
Derivatives | 10 \sin{(x )} - 1 | 10 \cos{(x )} |
Derivatives | 4 \cos{(x )} + 2 | - 4 \sin{(x )} |
Derivatives | 2 \cos{(x )} - 1 | - 2 \sin{(x )} |
Derivatives | 8 e^{x} - 3 | 8 e^{x} |
Derivatives | x^{3} + 7 | 3 x^{2} |
Derivatives | 9 e^{x} - 3 | 9 e^{x} |
Derivatives | 9 \tan{(x )} + 2 | \frac{9}{\cos^{2}{(x )}} |
Derivatives | 10 \sqrt{x} | \frac{5}{\sqrt{x}} |
Derivatives | 9 \log{(x )} + 1 | \frac{9}{x} |
Derivatives | 6 \cos{(x )} - 3 | - 6 \sin{(x )} |
Derivatives | 5 \sqrt{x} - 6 | \frac{5}{2 \sqrt{x}} |
Derivatives | 2 x^{5} + 1 | 10 x^{4} |
Derivatives | 3 x^{5} - 1 | 15 x^{4} |
Derivatives | 6 \sin{(x )} + 9 | 6 \cos{(x )} |
Derivatives | 6 e^{x} + 3 | 6 e^{x} |
Derivatives | 2 \sqrt{x} - 3 | \frac{1}{\sqrt{x}} |
Derivatives | 5 x^{2} + 9 | 10 x |
Derivatives | 8 \sin{(x )} - 7 | 8 \cos{(x )} |
Derivatives | 4 \sin{(x )} - 4 | 4 \cos{(x )} |
Derivatives | e^{x} + 3 | e^{x} |
Derivatives | 6 \log{(x )} | \frac{6}{x} |
Derivatives | 2 \sqrt{x} - 10 | \frac{1}{\sqrt{x}} |
Derivatives | 9 x^{3} + 6 | 27 x^{2} |
Derivatives | 2 \sqrt{x} + 6 | \frac{1}{\sqrt{x}} |
Derivatives | 6 x^{5} + 6 | 30 x^{4} |
Derivatives | \cos{(x )} - 1 | - \sin{(x )} |
Derivatives | 5 e^{x} + 9 | 5 e^{x} |
Derivatives | e^{x} + 9 | e^{x} |
Derivatives | 7 \sqrt{x} + 6 | \frac{7}{2 \sqrt{x}} |
Derivatives | 10 \cos{(x )} - 3 | - 10 \sin{(x )} |
Derivatives | 6 \log{(x )} + 3 | \frac{6}{x} |
Derivatives | 4 \log{(x )} - 1 | \frac{4}{x} |
Derivatives | 7 \log{(x )} - 9 | \frac{7}{x} |
Derivatives | 8 \sin{(x )} + 7 | 8 \cos{(x )} |
Derivatives | \frac{10 x + 47}{x + 4} | - \frac{7}{(x + 4)^{2}} |
Derivatives | 3 \sqrt{x} - 2 | \frac{3}{2 \sqrt{x}} |
Derivatives | 4 \sqrt{x} + 2 | \frac{2}{\sqrt{x}} |
Derivatives | 5 e^{x} + 6 | 5 e^{x} |
Derivatives | 8 x^{3} - 7 | 24 x^{2} |
Derivatives | 3 \log{(x )} - 7 | \frac{3}{x} |
Derivatives | 9 \cos{(x )} + 2 | - 9 \sin{(x )} |
Derivatives | 7 \sqrt{x} + 1 | \frac{7}{2 \sqrt{x}} |
Derivatives | 4 \sqrt{x} + 7 | \frac{2}{\sqrt{x}} |
Derivatives | \frac{- 9 x - 4}{x + 1} | - \frac{5}{(x + 1)^{2}} |
Derivatives | \frac{9 (x + 6)}{x + 5} | - \frac{9}{(x + 5)^{2}} |
Derivatives | 8 e^{x} - 5 | 8 e^{x} |
Derivatives | \frac{2 (x + 7)}{x + 2} | - \frac{10}{(x + 2)^{2}} |
Derivatives | 2 \tan{(x )} + 2 | \frac{2}{\cos^{2}{(x )}} |
Derivatives | 3 \cos{(x )} - 1 | - 3 \sin{(x )} |
Derivatives | 9 \cos{(x )} + 8 | - 9 \sin{(x )} |
Derivatives | 10 x - 1 | 10 |
Derivatives | e^{x} - 4 | e^{x} |
Derivatives | 6 \log{(x )} | \frac{6}{x} |
Derivatives | 5 \sqrt{x} - 8 | \frac{5}{2 \sqrt{x}} |
Derivatives | 6 \log{(x )} + 4 | \frac{6}{x} |
Derivatives | 4 \tan{(x )} + 6 | \frac{4}{\cos^{2}{(x )}} |
Derivatives | 2 \tan{(x )} - 1 | \frac{2}{\cos^{2}{(x )}} |
Derivatives | 8 \sin{(x )} + 4 | 8 \cos{(x )} |
Derivatives | 10 \log{(x )} + 10 | \frac{10}{x} |
Derivatives | \frac{5 - x}{x + 1} | - \frac{6}{(x + 1)^{2}} |
Derivatives | 9 \sqrt{x} - 5 | \frac{9}{2 \sqrt{x}} |
Derivatives | 6 e^{x} - 8 | 6 e^{x} |
Derivatives | \cos{(x )} - 5 | - \sin{(x )} |
Derivatives | 3 e^{x} + 7 | 3 e^{x} |
Derivatives | \frac{2 \cdot (2 x + 15)}{x + 5} | - \frac{10}{(x + 5)^{2}} |
Derivatives | 5 e^{x} - 8 | 5 e^{x} |
Derivatives | 10 \tan{(x )} - 1 | \frac{10}{\cos^{2}{(x )}} |
Derivatives | 10 \tan{(x )} + 2 | \frac{10}{\cos^{2}{(x )}} |
Derivatives | 8 \log{(x )} + 4 | \frac{8}{x} |
Derivatives | 9 \tan{(x )} + 9 | \frac{9}{\cos^{2}{(x )}} |
Derivatives | 5 \tan{(x )} + 9 | \frac{5}{\cos^{2}{(x )}} |
Derivatives | 5 x^{2} + 1 | 10 x |
Derivatives | \log{(x )} + 7 | \frac{1}{x} |
Derivatives | 8 x - 10 | 8 |
Derivatives | 2 \sqrt{x} | \frac{1}{\sqrt{x}} |
Derivatives | 5 \sqrt{x} + 4 | \frac{5}{2 \sqrt{x}} |
Derivatives | 3 \tan{(x )} - 5 | \frac{3}{\cos^{2}{(x )}} |
Derivatives | 9 \tan{(x )} - 1 | \frac{9}{\cos^{2}{(x )}} |
Derivatives | \tan{(x )} + 1 | \frac{1}{\cos^{2}{(x )}} |
Derivatives | \tan{(x )} + 6 | \frac{1}{\cos^{2}{(x )}} |
Derivatives | 7 \sqrt{x} - 10 | \frac{7}{2 \sqrt{x}} |
Derivatives | 6 \sqrt{x} - 2 | \frac{3}{\sqrt{x}} |
Derivatives | \cos{(x )} - 9 | - \sin{(x )} |
Derivatives | 4 \sqrt{x} + 9 | \frac{2}{\sqrt{x}} |
Derivatives | 8 x + 2 | 8 |
Derivatives | \tan{(x )} + 7 | \frac{1}{\cos^{2}{(x )}} |
Derivatives | 10 x^{4} + 7 | 40 x^{3} |
Derivatives | x - 4 | 1 |
Derivatives | 8 x - 8 | 8 |
Derivatives | 10 \log{(x )} - 7 | \frac{10}{x} |
Derivatives | 5 \tan{(x )} + 5 | \frac{5}{\cos^{2}{(x )}} |
Derivatives | 7 \sqrt{x} - 2 | \frac{7}{2 \sqrt{x}} |
Derivatives | 3 \cos{(x )} + 3 | - 3 \sin{(x )} |
Derivatives | 5 \log{(x )} | \frac{5}{x} |
Derivatives | \frac{3 (x + 4)}{x + 3} | - \frac{3}{(x + 3)^{2}} |
Derivatives | x^{3} | 3 x^{2} |
Derivatives | 3 x + 7 | 3 |
Derivatives | 2 x^{4} + 9 | 8 x^{3} |
Symbolic calculus training pool
Single variable calculus exercises with closed form answers: derivatives of composite expressions, indefinite and definite integrals, limits of indeterminate forms, and coefficients of Maclaurin series, with some multivariable operators in one of the sources. A set generated for this pool and two public datasets read at the pinned revisions named below, laid out twice. Train on either layer or on both.
pool.jsonl
Every source rewritten into one shape, 1529662 rows, one JSON object per line, with these fields.
| Field | What it holds |
|---|---|
id |
a row identifier unique within this file |
question |
the problem, as it would be put to a model |
answer |
the answer its source publishes, in LaTeX, or null |
expression |
the same answer in sympy syntax, present only when it was checked |
family |
derivative, second_derivative, indefinite_integral, definite_integral, limit, taylor_coefficient, or null |
variable |
the letter the problem is written in, or null |
mode |
expression, or antiderivative when an additive constant is free, or null when the row was not read as one of the families |
category |
the family and tier for generated rows, the source's own label otherwise |
source |
the name of the source directory the row came from |
source_split, source_row |
where the row sits in that set |
provenance_class |
how the row came to exist |
licence |
the licence of the source it came from |
1076913 of the rows carry a checked answer in expression. A checked answer is one that was
compared with an answer worked out here by a computer algebra system, under a symbolic
equivalence: the two sides are evaluated at random points at fifty digits and the difference is
simplified where the points cannot decide. A derivative is checked by differentiating the
function, an integral by differentiating the published answer and comparing it with the integrand,
a limit by taking the limit. A null expression means the answer was not checked, usually because
the question is of a kind this check does not cover or because its notation is one the checker
does not read, and it is not evidence that the answer is wrong.
Rows are deduplicated on the canonical form of the question, which is the kind of question together with the expression it is about in a computer algebra system's own canonical representation, keeping the first source that carries it in the order of the sections below. Rows whose question could not be read that way are kept as they come.
The generated rows are spread over families and tiers as below, where the tier is how deep the composition or how many terms the integrand has. The limit rows saturate: the table of indeterminate forms behind them is small, so those cells hold every problem they can rather than their share of the mix.
| Category | Rows |
|---|---|
definite_integral/t1 |
39882 |
definite_integral/t2 |
156384 |
definite_integral/t3 |
39271 |
derivative/t1 |
138025 |
derivative/t2 |
153478 |
derivative/t3 |
41278 |
indefinite_integral/t1 |
13470 |
indefinite_integral/t2 |
155040 |
indefinite_integral/t3 |
39252 |
limit/t1 |
1128 |
limit/t2 |
1148 |
limit/t3 |
1189 |
taylor_coefficient/t1 |
96926 |
taylor_coefficient/t2 |
99065 |
taylor_coefficient/t3 |
24463 |
sources/
The same data untouched, 1543932 rows, one directory per source. The downloaded sets hold the files at the paths, in the format and with the columns their own repositories publish, and the generated set is one jsonl file. Nothing here was renamed, reshaped, reordered or deduplicated. Use this layer if you want a field the rewritten one drops, such as the chat framing and the subtopic labels of the largest source.
The sources
sources/generated
Single variable calculus problems drawn from the package's own grammars: the derivative of a composition, an antiderivative, a definite integral over a bounded interval, a limit of an indeterminate form, and one coefficient of a Maclaurin series, each with its answer in closed form.
Generated for this pool under seed 20260914, file problems.jsonl. 999999 rows here, of which
999999 also appear in pool.jsonl and 999999 of those carry a checked answer. Provenance class
rule-generated, licence mit. Its own fields are id, question, answer, expression, family,
tier, variable, mode, category.
Worth knowing. One generator drew all of it, so it is one distribution rather than a survey of exercise styles, and its families and tiers follow the weights recorded in the manifest rather than a uniform spread. Its limit problems saturate: the table of indeterminate forms behind them is small, so that cell holds every problem it can rather than its share of the mix.
sources/amps_calculus
540000 calculus exercises in a chat format, fourteen kinds: differentiation, second derivatives, integration, series expansions and coefficients, arclength, and the vector calculus operators (gradient, divergence, curl, laplacian, jacobian). The card names the AMPS problem collection as the source, which built them from exercise templates with a computer algebra system.
From NecroMOnk/khan-math-calculus at revision 6f06bc2033953307f10a9e6ba184482cac38bfc6, files
data/khan-math-calculus.jsonl. 539933 rows here, of which 526107 also appear in pool.jsonl and
74856 of those carry a checked answer. Provenance class rule-generated, licence mit. Its own
fields are messages for the chat turns (a fixed system line, the problem, the answer), topic,
subtopic.
Worth knowing. The licence is the uploader's tag and the chain behind it runs through the AMPS release to exercise templates that are not the uploader's work, so the term is asserted rather than verified here. Its notation is the one a well known computer algebra system prints, so an inverse function is written as a power of minus one and a root as a bracketed radical, which this builder's checker does not read: that is why most of its rows ship with an unchecked answer. Its series questions are not always self-consistent, an expansion asked for around one point and answered around another, which is one more reason those rows are not checked.
sources/calculus_qa
4000 exercises in four equal types, derivatives, integrals, limits and first and second order differential equations, each a bare expression in LaTeX with its answer in LaTeX. The shapes and the spelling are those of a script over a computer algebra system.
From di-zhang-fdu/calculus-dataset at revision 89fb7a574655a11b8db55a3b9e3fe208e14996d7, files
data/train-00000-of-00001.parquet. 4000 rows here, of which 3556 also appear in pool.jsonl and
2058 of those carry a checked answer. Provenance class rule-generated, licence mit. Its own
fields are type for the kind of exercise, q for the expression, a for the answer.
Worth knowing. It publishes a type and an expression rather than a question, so the one line of instruction in front of each problem in the curated layer is written by this builder and the raw layer keeps the two columns as they are. A few of its limits do not exist and are answered with an interval of oscillation, which the check rejects, so those rows ship unchecked.
Provenance and licences
Every row of this pool is rule-generated, which is the honest headline: there is no large human- written calculus exercise corpus with a licence that allows redistribution. The generated layer comes from a program that draws an expression and works out the answer with a computer algebra system. The largest downloaded source comes from exercise templates, written by people, filled in and solved by a computer algebra system, which is the one human signal anywhere in the pool. The smallest comes from a script over the same kind of system. No row anywhere in the pool was written by a language model.
The pool as a whole is offered under mit. Both downloaded sources are mit and the generated part
is released under mit as well, and every rewritten row carries its own term in the licence field
while each directory under sources/ is one source, so a subset under a single licence can be
selected.
Filtering
67 rows of the downloaded sources were removed while this pool was assembled, from both layers
alike, so their counts here do not match the totals their publishers state: 16 on the canonical
form of the question and 51 on a shared run of eight words. 106 generated draws were discarded on
the same run-of-eight-words rule and redrawn, which moves no count. A few exercises of one
downloaded source carry a computer algebra system's failure token (ComplexInfinity, Indeterminate,
Aborted) where an answer should be: 613 rows ship here with a null answer and no expression,
and 824 rows whose question itself carries the token are left out of this file. The raw layer
keeps all of them as published. Nothing else was filtered: no family, no tier and no difficulty
was selected for or against, so the category and family fields are how to select what you
want.
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