Datasets:
image imagewidth (px) 148 5.28k | text stringlengths 10 1.96k | bucket stringclasses 4
values | char_len int64 10 1.96k |
|---|---|---|---|
\lim_{x \to a} \arctan\left(5x\right) | normal | 37 | |
F = \int \left( 7u^{3} \sqrt{9u - 1u^{3}} + e^{3u} + 7u^{4} + 3u^{3} + 5u^{3} + 3u^{2} \right)\, du + \sum_{n=1}^{\infty} \frac{4n}{6n^{2}} | medium | 139 | |
\int_{a}^{T} \left( 2u^{2} \frac{8u^{2} + 7}{3u^{5}} \right)\, du = 6x - 5x^{2} - 2 | medium | 83 | |
\frac{d}{dx}\left[ 5x^{2} e^{9x^{2}} \right] = 8x^{3} - 9 | normal | 57 | |
f(x) = 1x - 6x^{2} | normal | 18 | |
F = \sum_{n=1}^{N} \frac{3n^{5}}{5n^{5}} + \sum_{m=0}^{n} 4m - \int_{1}^{1} \left( 8t^{2} \cosh\left(t^{5}\right) - \sinh\left(3t^{3}\right) - \sqrt{5t^{5} - 5} - 6t^{2} \sqrt{7t^{2}} - 3t - 7t - 8t + 9t - 2t^{2} - \frac{1}{4t^{3} - 2} \right)\, dt | long | 248 | |
\frac{d}{dt}\left[ 6t^{4} + 9t^{5} + 1t^{4} \right] | normal | 51 | |
F = \int \left( e^{-8u} - 4u + 4u - 6 - 8u^{3} \sqrt{9u^{2}} - 2u \sinh\left(7u^{3}\right) - 1u - 4u^{2} - 5u - 5u + 3u - 2 \right)\, du + \frac{d^{2}}{dx^{2}}\left( \frac{1x^{2}}{9x + 9x^{2}} \right) = 8x - 1x + 2 + \frac{2x^{5}}{3x^{5} - 5x^{3}} | long | 247 | |
y = e^{4x} | normal | 10 | |
\sum_{n=1}^{n} 4x^{n} | normal | 21 | |
\sum_{n=1}^{N} 1q^{n} | normal | 21 | |
y = \sqrt{7x^{2} - 7x^{4}} | normal | 26 | |
\frac{d}{dt}\left[ 1t - 2 \right] | normal | 33 | |
y = \sqrt{8x^{2} + 8} | normal | 21 | |
f(x) = 2x^{2} + 7x^{2} | normal | 22 | |
f(x) = 6x^{3} - 7x | normal | 18 | |
\frac{d}{dt}\left[ \sinh\left(5t^{3}\right) - 2t^{2} \sqrt{8t^{4} - 5t^{4}} - 8t^{2} \frac{3t}{7t^{2} + 2t^{5}} - \sin\left(2t\right) - 7t^{2} - 3t - t^{2} - 8 - 7t^{2} + 8t - 5 - \frac{1t^{2}}{4t^{2} + 3t^{5}} \right] | long | 218 | |
\int_{-\infty}^{\pi} \left( 3t^{3} - 5t^{3} + 5 \right)\, dt = 9x^{3} + 8x^{2} + 9 | medium | 82 | |
f(x) = 6x + 5x^{4} + 3x | normal | 23 | |
\frac{d^{3}}{dt^{3}}\left( \sqrt{2t - 3t^{2}} \right) = 4x - 4x^{3} + 3 | normal | 71 | |
\begin{aligned} I = \int \left( 2 x^{4} + x^{2} e^{x} + x e^{x} + 2 e^{3 x} + 11 e^{2 x} + 8 \sin{\left(2 x \right)} + 2 \sin{\left(4 x \right)} + 9 \cos{\left(2 x \right)} + 15 \cos{\left(3 x \right)} + \frac{7}{x^{3}} \right)\, dx \\ \int 2 e^{3 x}\, dx = \frac{2 e^{3 x}}{3} \\ \int 6 \cos{\left(3 x \right)}\, dx = 2... | derivation | 1,267 | |
\int_{a}^{\infty} \left( 2u^{2} \right)\, du = 5x^{5} | normal | 53 | |
f(x) = x^{3} - 7x^{2} | normal | 21 | |
\frac{d^{3}}{dx^{3}}\left( \frac{5x^{2} - 4}{2x - 6x^{5}} \right) | normal | 65 | |
\begin{aligned} I = \int \left( 6 x^{3} + 7 x^{2} e^{x} + 7 x^{2} + x e^{x} + 2 e^{x} + 3 \sin{\left(x \right)} + \sin{\left(2 x \right)} + 4 \sin{\left(3 x \right)} + 6 \cos{\left(x \right)} + 8 \cos{\left(2 x \right)} + \frac{5}{x} + \frac{1}{x^{2}} + \frac{8}{x^{3}} \right)\, dx \\ \int 6 x^{3}\, dx = \frac{3 x^{4}}... | derivation | 1,385 | |
y = e^{-6x^{5}} | normal | 15 | |
\frac{d}{dt}\left[ \frac{1t^{4}}{6t^{4} + 7t^{2}} \right] = 2x^{5} + 3 | normal | 70 | |
\frac{d}{dt}\left[ t^{5} - t + 2t^{3} - 5 + 2t \frac{1}{6t^{5} - 5} + 2t^{4} \arctan\left(5t^{3}\right) + 8t^{2} - 9 + \frac{t^{2}}{6t^{4}} + \frac{1}{t^{3}} \right] | medium | 165 | |
\begin{aligned} I = \int \left( 6 x^{4} + 3 x^{2} e^{x} + 4 x^{2} + 8 x e^{x} + 16 e^{2 x} + 8 e^{x} + 6 \sin{\left(2 x \right)} + 5 \sin{\left(3 x \right)} + 8 \cos{\left(3 x \right)} \right)\, dx \\ \int 5 \sin{\left(3 x \right)}\, dx = - \frac{5 \cos{\left(3 x \right)}}{3} \\ \int 8 e^{2 x}\, dx = 4 e^{2 x} \\ \int ... | derivation | 1,583 | |
\sum_{n=1}^{N} \frac{4n}{4n - 3n} | normal | 33 | |
\sum_{n=1}^{n} 7x^{n} = 5x^{2} + 8 | normal | 34 | |
f(x) = 6x^{5} + x^{5} + 9x | normal | 26 | |
\begin{aligned} I = \int \left( x^{2} e^{x} + 6 x e^{x} + e^{3 x} + 2 e^{2 x} + 8 e^{x} + \sin{\left(2 x \right)} + 5 \sin{\left(4 x \right)} \right)\, dx \\ \int 6 x e^{x}\, dx = \left(6 x - 6\right) e^{x} \\ \int 8 e^{x}\, dx = 8 e^{x} \\ \int x^{2} e^{x}\, dx = \left(x^{2} - 2 x + 2\right) e^{x} \\ \int 2 e^{2 x}\, ... | derivation | 730 | |
F = \int_{-\infty}^{2\pi} \left( 9x^{2} \frac{1}{4x^{3} + 6} + 8x + 5x^{2} + 9x^{2} + \ln\left(6x^{3}\right) + 3x^{2} + 9x^{4} - 2 + 4x^{4} + 5x + \frac{x^{2} - 9}{8x - 5x^{5} - 4} + 2x \frac{5x - 4}{x^{2} - 7x^{3} + 5} \right)\, dx - \int_{1}^{n} \left( 8u^{5} - 6u^{4} - 8u + 9u \frac{6u^{3} + 2}{3u^{2} - 3u} + \ln\le... | long | 471 | |
F = \int \left( 8t^{3} \sqrt{3t} - e^{8t^{3}} - t e^{5t} - 3t - 9t^{2} \sqrt{3t^{3} + 7t} \right)\, dt + \frac{d}{dx}\left[ \arctan\left(1x^{2}\right) - \frac{1}{4x^{2}} - \sqrt{3x^{4}} - 3x^{5} - 2x - 4x^{2} - 8 - \frac{1}{2x^{2} + 3x} - \arctan\left(4x^{4}\right) - 2x^{2} \right] + \int_{-\infty}^{\infty} \left( 2u^{... | long | 521 | |
f(x) = 4x^{2} - x^{2} + 4 | normal | 25 | |
\frac{d}{dt}\left[ t e^{9t^{2}} \right] | normal | 39 | |
\int \left( 8x^{3} \right)\, dx = 3x - 2 | normal | 40 | |
\lim_{x \to \infty} \sqrt{8x^{3}} | normal | 33 | |
\sum_{n=1}^{\infty} \frac{5n}{6n^{4}} | normal | 37 | |
y = e^{4x^{3}} | normal | 14 | |
F = \int \left( 2x^{2} + 4x^{2} \ln\left(4x^{2}\right) + \tan\left(3x^{3}\right) + e^{-1x} \right)\, dx + \frac{d}{dt}\left[ \sqrt{2t^{2} - 9} \right] + \int \left( 3x^{2} \cos\left(x^{5}\right) - \frac{2x - 7}{7x^{3} - 9x + 9} - 9x^{2} \sqrt{4x + 8x} - 3x - 1 - 5x^{2} \frac{1}{6x - 7} - 3x^{2} + 8x^{2} - 5x^{2} - 3x^{... | long | 360 | |
\frac{d}{dx}\left[ 9x + 2x^{2} \right] | normal | 38 | |
\frac{d^{2}}{dt^{2}}\left( \frac{2t^{2} - 1}{7t - 2t^{2}} \right) | normal | 65 | |
\lim_{x \to 0} \frac{5x}{6x^{2}} = 3x^{2} | normal | 41 | |
\lim_{x \to 1} \sqrt{3x^{2} - 5x - 3} = 4x^{3} | normal | 46 | |
\lim_{x \to 1} e^{-3x^{2}} | normal | 26 | |
\lim_{x \to 0} \tan\left(2x^{5}\right) = 2x^{4} - 8x^{4} | normal | 56 | |
\sum_{n=1}^{n} \frac{9n^{3}}{5n^{4} - 8n^{2}} = 2x^{3} - 5 | normal | 58 | |
f(x) = 2x^{3} + x - 4x^{2} - 4 | normal | 30 | |
f(x) = 9x^{2} + 2x - 8 | normal | 22 | |
\int_{1}^{\pi} \left( 7u^{3} + 2u^{2} - 5u - 9 \right)\, du | normal | 59 | |
\int \left( 4x^{3} - 6x^{5} \right)\, dx = 4x | normal | 45 | |
\lim_{x \to \infty} \arctan\left(8x^{2}\right) = 8x^{4} | normal | 55 | |
F = \sum_{n=1}^{N} \frac{6n}{8n^{2} - 3} + \sum_{m=0}^{n} 6m^{2} = 4x^{5} - 1x^{3} - 7x^{2} - \frac{2x^{2}}{9x^{5}} | medium | 115 | |
f(x) = 7x + 7x^{2} | normal | 18 | |
F = \int \left( 6t^{2} \tan\left(9t^{3}\right) + 6t^{3} \frac{1}{9t^{2} - 8t^{2}} + 3t + t^{3} - 6t^{3} + \frac{1}{t - 8t} + 6t^{2} \ln\left(2t^{2}\right) \right)\, dt - \int \left( 3t^{2} - 6t^{2} + 1t^{2} + \frac{2t^{3}}{9t + 4t^{4}} + 1t \frac{6t}{2t + 3t^{2} + 8} + 8t^{2} + 7 + 2t^{4} \frac{1}{2t^{2}} \right)\, dt | long | 319 | |
y = \frac{1}{9x^{3} - 9} | normal | 24 | |
\lim_{x \to a} \arctan\left(5x^{2}\right) = 5x^{2} | normal | 50 | |
\frac{d^{2}}{dt^{3}}\left( \sqrt{1t^{3} + t + 7} \right) | normal | 56 | |
F = \int \left( 4t^{4} \sqrt{1t^{4} + 7t} + e^{-5t} + \sqrt{t^{4} + 5t^{2}} + 4t^{2} \frac{8t - 5}{9t^{2}} + \ln\left(5t^{2}\right) \right)\, dt - \frac{d^{3}}{dx^{2}}\left( \cos\left(6x^{2}\right) \right) - \sum_{n=1}^{\infty} \frac{2n^{2}}{8n} | long | 245 | |
\begin{aligned} I = \int \left( 15 x^{5} + e^{3 x} + 4 e^{2 x} + 2 \sin{\left(3 x \right)} + 2 \cos{\left(x \right)} + 8 \cos{\left(2 x \right)} + 5 \cos{\left(3 x \right)} + 2 \cos{\left(4 x \right)} + \frac{8}{x^{3}} \right)\, dx \\ \int 2 \sin{\left(3 x \right)}\, dx = - \frac{2 \cos{\left(3 x \right)}}{3} \\ \int 5... | derivation | 1,674 | |
\begin{aligned} I = \int \left( 7 x^{2} e^{x} + 6 x + e^{3 x} + \sin{\left(2 x \right)} + 5 \sin{\left(4 x \right)} + 4 \cos{\left(4 x \right)} \right)\, dx \\ \int 3 x^{2} e^{x}\, dx = \left(3 x^{2} - 6 x + 6\right) e^{x} \\ \int \sin{\left(2 x \right)}\, dx = - \frac{\cos{\left(2 x \right)}}{2} \\ \int 5 \sin{\left(4... | derivation | 767 | |
\lim_{x \to 0} e^{-2x^{3}} = 1x | normal | 31 | |
\sum_{n=1}^{n} 7q^{n} | normal | 21 | |
f(x) = 5x^{5} + 7x^{2} - 6x | normal | 27 | |
F = \int_{-a}^{\pi} \left( 4t^{3} \frac{1}{9t + 8t} + e^{-6t^{2}} + 6t^{4} \sqrt{2t^{4} + 8} + 6t^{4} \cosh\left(3t^{3}\right) + 8t^{2} - 5t^{5} + 2t^{3} + 5t^{2} + 6 + \sinh\left(5t\right) \right)\, dt - \int_{1}^{b} \left( \sqrt{5u} + 8u^{2} - 2u^{2} - 6u^{4} + 2 + e^{2u^{4}} + 5u \frac{1}{7u^{4}} + \sqrt{9u^{4} + 6}... | long | 400 | |
\frac{d^{3}}{dx^{3}}\left( \sinh\left(8x^{5}\right) \right) | normal | 59 | |
F = \int \left( 7x^{3} \sinh\left(2x^{4}\right) - 3x^{2} - x^{4} - 5 - 4x^{5} + 3x^{3} - 4x^{2} - 9x^{2} + 7x^{5} - 6 - \sqrt{3x^{2}} \right)\, dx = 9x^{2} + 6x^{5} + e^{7x} | medium | 173 | |
F = \sum_{n=1}^{\infty} \frac{5n}{6n^{3}} + \sum_{m=0}^{n} 1m - \sum_{n=1}^{n} \frac{4n^{2}}{3n^{5}} | medium | 100 | |
\frac{d^{3}}{dt^{3}}\left( e^{-1t^{5}} \right) | normal | 46 | |
\begin{aligned} I = \int \left( 4 e^{3 x} + 8 e^{2 x} + 8 \sin{\left(2 x \right)} + 2 \sin{\left(4 x \right)} + 8 \cos{\left(4 x \right)} + \frac{11}{x} + \frac{5}{x^{2}} \right)\, dx \\ \int \frac{5}{x^{2}}\, dx = - \frac{5}{x} \\ \int 2 \sin{\left(4 x \right)}\, dx = - \frac{\cos{\left(4 x \right)}}{2} \\ \int 8 \sin... | derivation | 1,308 | |
F = \int_{0}^{a} \left( 8u^{2} \sqrt{6u^{3} + 8u^{3}} + e^{3u^{5}} + \tan\left(4u^{2}\right) + e^{-8u^{3}} + 8u^{3} - 4u^{2} \right)\, du - \sum_{n=1}^{n} \frac{4n^{3}}{1n^{3} - 8n + 8} | long | 185 | |
f(x) = 3x - 5x^{3} - 1 | normal | 22 | |
y = \ln\left(3x\right) | normal | 22 | |
\frac{d}{dx}\left[ 9x^{5} \sqrt{x} \right] | normal | 42 | |
f(x) = 9x^{2} - 5x - 7 | normal | 22 | |
F = \int \left( 5t \cosh\left(4t^{4}\right) - \frac{6t^{5}}{5t} - \sinh\left(7t^{4}\right) - 6t^{2} + 8t - t^{4} + 5t - 9t^{4} \frac{1}{t^{2} - 4t^{2} + 7} \right)\, dt + \int \left( 5x^{2} e^{8x^{4}} + 4x^{5} \sinh\left(8x^{3}\right) + \tan\left(3x^{5}\right) + \frac{1}{7x + 8x + 3} + 3x^{3} - 3 + \sin\left(2x^{2}\rig... | long | 336 | |
\begin{aligned} I = \int \left( 10 x^{3} + 3 x^{2} e^{x} + 8 x e^{x} + 7 e^{2 x} + 17 e^{x} + 4 \sin{\left(3 x \right)} \right)\, dx \\ \int 8 x e^{x}\, dx = \left(8 x - 8\right) e^{x} \\ \int 4 \sin{\left(3 x \right)}\, dx = - \frac{4 \cos{\left(3 x \right)}}{3} \\ \int 9 e^{x}\, dx = 9 e^{x} \\ \int 3 x^{2} e^{x}\, d... | derivation | 719 | |
F = \int_{-a}^{2\pi} \left( 8t^{3} - e^{t^{2}} - 2t^{3} - 4t - \frac{8t + 8}{7t^{2}} - 4t \sqrt{3t - 3} - 7t^{2} \frac{1}{7t} \right)\, dt = 2x + 1x - \frac{3x^{3} + 9}{2x} | medium | 172 | |
\int \left( \arctan\left(1x^{2}\right) \right)\, dx | normal | 51 | |
\frac{d}{dt}\left[ t \sin\left(5t\right) \right] | normal | 48 | |
\frac{d}{dt}\left[ 8t \frac{8t - 1}{7t^{5} + 4t^{3}} \right] | normal | 60 | |
\begin{aligned} I = \int \left( 3 x^{3} + 8 x^{2} + 24 x e^{x} + 5 \sin{\left(x \right)} + 2 \cos{\left(3 x \right)} \right)\, dx \\ \int 9 x e^{x}\, dx = \left(9 x - 9\right) e^{x} \\ \int 6 x e^{x}\, dx = \left(6 x - 6\right) e^{x} \\ \int 5 \sin{\left(x \right)}\, dx = - 5 \cos{\left(x \right)} \\ \int 2 \cos{\left(... | derivation | 1,001 | |
F = \sum_{n=1}^{n} \frac{5n^{2}}{n^{2} - 9} + \sum_{m=0}^{N} 3m^{4} + \sum_{n=1}^{n} \frac{3n^{3}}{5n} | medium | 102 | |
\begin{aligned} I = \int \left( 2 x^{5} + 8 x^{2} e^{x} + 2 x e^{x} + 9 e^{3 x} + 4 e^{2 x} + 3 \sin{\left(x \right)} + 7 \sin{\left(3 x \right)} + 2 \cos{\left(x \right)} + 14 \cos{\left(4 x \right)} + \frac{4}{x^{2}} + \frac{9}{x^{3}} \right)\, dx \\ \int 2 \cos{\left(x \right)}\, dx = 2 \sin{\left(x \right)} \\ \int... | derivation | 1,959 | |
F = \int \left( \frac{7t^{2}}{3t^{5} + 6} - \sin\left(1t\right) - 9t \frac{3t^{2}}{8t^{4} + 2} - 9t^{2} - 9t - 3t + 5t + 4 - 2t^{2} e^{7t^{4}} - 8t^{2} \sqrt{8t^{3} + 5} \right)\, dt - \int_{0}^{b} \left( 8x + \sqrt{3x^{3} - 6x} + e^{9x^{2}} + 9x^{2} + 6 + 4x^{2} \frac{6x}{6x + 1} + 6x^{2} + 1x^{3} \right)\, dx | long | 312 | |
F = \int_{-\infty}^{\infty} \left( e^{1u} - 6u + 2u^{2} - 6 - 9u - 4u^{2} - 3u^{2} \frac{1}{3u^{3} + 3u^{2}} - 5u^{3} - 2u - 3u e^{-8u^{3}} \right)\, du + \int \left( 9t + 2t^{2} - 4 + 6t + 8t + 9t^{4} \arctan\left(6t^{4}\right) + 7t + 7t - 2t^{2} \right)\, dt | long | 260 | |
F = \int_{-a}^{1} \left( 6u^{5} + 4u^{3} - 4u^{4} - 9 - 6u^{4} e^{2u^{3}} - \sqrt{7u^{2}} - 7u^{2} + 7u^{3} - 2u^{3} e^{5u} - 3u \right)\, du + \int \left( 5t^{5} + 3t e^{-6t^{2}} + 1t^{2} - 6t^{3} + 8t^{2} \frac{2t}{7t^{4}} + 5t^{3} + 7t^{2} - 5t^{3} + 4t \frac{7t^{2}}{t^{3} - 1} \right)\, dt + \sum_{n=1}^{\infty} \fr... | long | 341 | |
\sum_{n=1}^{\infty} r^{n} = 8x^{2} - 8x^{5} | normal | 43 | |
\begin{aligned} I = \int \left( 2 x e^{x} + 4 x + 2 \sin{\left(3 x \right)} + 10 \cos{\left(3 x \right)} \right)\, dx \\ \int 3 \cos{\left(3 x \right)}\, dx = \sin{\left(3 x \right)} \\ \int x\, dx = \frac{x^{2}}{2} \\ \int 3 x\, dx = \frac{3 x^{2}}{2} \\ \int 2 \sin{\left(3 x \right)}\, dx = - \frac{2 \cos{\left(3 x \... | derivation | 599 | |
f(x) = 4x^{3} + 5x^{3} + 5x - 6 | normal | 31 | |
\int_{a}^{2\pi} \left( x^{4} + 6x + 5x^{2} - 1 \right)\, dx | normal | 59 | |
y = \frac{8x^{2} + 8}{x^{2} - 7x^{4}} | normal | 37 | |
F = \int \left( 4t^{3} e^{-3t^{2}} + \cosh\left(9t\right) + \sinh\left(3t\right) + \frac{1}{5t^{3}} + 5t^{3} \frac{1}{5t^{2}} + t^{2} \frac{1}{1t^{3}} \right)\, dt = 4x - 5x^{2} - 4 + \sqrt{4x^{3} - 7} | long | 201 | |
y = \sqrt{9x^{5}} | normal | 17 | |
F = \int_{a}^{\infty} \left( 5x - \frac{x}{6x^{5} - 1x^{2} + 1} - 2x^{3} \frac{8x + 6}{1x^{4}} - 9x^{3} \tan\left(5x^{3}\right) - 6x - 6x - 4x e^{-7x} \right)\, dx + \int_{0}^{2\pi} \left( 9u^{2} \frac{2u^{2}}{5u + 6u^{3} - 6} + 5u^{4} \sqrt{5u^{2} - 6u} + \sinh\left(u\right) + 1u^{4} e^{7u^{2}} + 2u^{5} - 1u^{3} + 7u^... | long | 387 | |
F = \int_{1}^{a} \left( 4x^{2} \sqrt{1x^{4} + 8} - \arctan\left(8x^{2}\right) - 6x^{4} + 8x^{2} + 3 - 9x^{3} \frac{1}{3x} - 6x^{2} + 8x^{2} + 4x^{2} \right)\, dx = 8x^{2} + x^{2} - \sqrt{9x^{4}} | long | 194 | |
\frac{d^{3}}{dt^{3}}\left( e^{4t^{2}} \right) | normal | 45 | |
F = \sum_{n=1}^{N} \frac{3n^{2}}{7n^{3} + n^{2} - 3} + \sum_{m=0}^{N} 1m^{3} + \int \left( \frac{1}{8u + 6} - \cos\left(3u\right) - \sinh\left(3u^{2}\right) - \frac{1}{8u^{2} + 7} \right)\, du | long | 192 |
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Formula OCR Synthetic Benchmark Dataset
Dataset Summary
Formula OCR Synthetic Benchmark Dataset is a synthetically rendered mathematical formula and calculus expression dataset built for training neural formula OCR decoders. It contains rendered formula snippets covering integration, differentiation, limits, summations, and matrix algebra.
Dataset Structure
- Format: PNG formula crop images + ground-truth LaTeX strings.
- Fields:
file: Path to formula crop image.text: LaTeX code for the formula.bucket: Sequence length category (normal,medium,long).
Usage
from datasets import load_dataset
dataset = load_dataset("Srijan-Upadhyay/formula-ocr-synth-bench")
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