LIME-DATA/ocrbench · Datasets at Hugging Face

dataset stringclasses 22 values	level stringclasses 3 values	question stringlengths 16 136	question_type stringclasses 10 values	question_id int64 0 998	answer listlengths 1 4	description stringlengths 158 1.42k
POIE	difficult	what is the value for Calories/Energy of per serving? Answer this question using the text in the image directly.	Key Information Extraction	897	[ "858", "206" ]	The image is a table comparing the nutritional values of two different types of food. The first column lists the type of nutrient, such as energy (kcal), fat, saturates, carbohydrates, sugars, and protein. The second column shows the per 100g values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The third column shows the per burger values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The fourth column shows the % as per instructions values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The fifth column shows the per 100g values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The sixth column shows the per burger values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food
POIE	difficult	what is the value for Sodium of per 100g/ml? Answer this question using the text in the image directly.	Key Information Extraction	899	[ "15mg", "15 mg" ]	The image is a nutrition label for a food product. It lists the calories per serving, which is 150 calories, and the percentage of daily value (% DV) for various nutrients. The nutrients listed include total fat, saturated fat, trans fat, cholesterol, sodium, total carbohydrates, dietary fiber, total sugars, and protein. Each nutrient has a corresponding amount per serving and a percentage of daily value based on a 2,000 calorie diet. The label also includes the amount of monounsaturated fat and polyunsaturated fat per serving.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	900	[ "y _ { 2 } = - 1\n", "y_2 = - 1\n" ]	The image shows a handwritten note with the letters "Y" and "E" written in black ink on a white background. The writing appears to be done with a pen or marker, and the letters are written in a cursive style. The "Y" is larger and more prominent than the "E," and both letters are connected at the top. The handwriting is slightly slanted to the right, giving it a dynamic and informal appearance.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	901	[ "x _ { 1 } = \\frac { - 2 + 2 \\sqrt { 2 } } { 2 }\n", "x_1 = \\frac { - 2 + 2 \\sqrt { 2 } } { 2 }\n" ]	The image shows a mathematical expression written in black ink on a white background. The expression appears to be a fraction with a numerator and a denominator. The numerator contains the number 3 and a plus sign, followed by another number which is not fully visible. The denominator contains the number 1. The overall expression seems to represent a simple algebraic fraction.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	902	[ "V = \\frac { F } { \\rho } = \\frac { 7 . 6 N } { 0 . 8 \\times 1 0 ^ { 3 } k g / m ^ { 2 } \\times 1 0 N / k g } = 0 . 9 5 \\times 1 0 ^ { - 3 } m ^ { 3 }\n", "V = \\frac { F } { \\rho } = \\frac { 7 . 6 N } { 0 . 8 \\times 1 0 ^3 k g / m^2 \\times 1 0 N / k g } = 0 . 9 5 \\times 1 0 ^ { - 3 } m^3\n" ]	The image shows a piece of paper with handwritten text in black ink. The text appears to be a mathematical equation or expression, as it includes the symbols "x" and "/". There is also a line drawn through the text, indicating that it may have been crossed out or marked for correction. The background of the paper is white, and there are grid lines visible, suggesting that the paper may be from a notebook or graph paper.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	904	[ "I _ { 2 } = \\frac { u } { R _ { 2 } } = \\frac { 6 V } { 1 0 \\Omega } = 0 . 6 A\n", "I _2= \\frac { u } { R_2} = \\frac { 6 V } { 1 0 \\Omega } = 0 . 6 A\n" ]	The image shows a handwritten mathematical equation. The equation is written in black ink on a white background. The equation reads "-2/6V". The number "-2" is written at the top left corner of the equation, and the fraction "1/6V" is written at the bottom right corner. The equation appears to be a ratio or proportion involving the number "-2" and the volume "6V". The handwriting is clear and legible, with the numbers and symbols properly spaced and aligned.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	905	[ "- 6 x = \\frac { 2 } { 3 } - 3 + 4\n" ]	The image shows a mathematical equation written in black ink on a white background. The equation is a fraction with the number 2 as the numerator and the number 3 as the denominator, separated by a horizontal line. The equation is centered in the image and takes up most of the space. The numbers are written in a simple, clear font that is easy to read. The overall appearance of the image is clean and minimalistic, with no additional decorations or embellishments.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	906	[ "\\frac { 6 . 8 } { x } = \\frac { 1 . 7 } { 4 }\n" ]	The image shows a handwritten mathematical equation on a white surface. The equation appears to be a fraction with the numerator being "1" and the denominator being "x^2 - 7x + 8". The handwriting is in black ink, and the equation is written in a cursive style. The background of the image is plain white, and there are no other objects or elements present in the image.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	909	[ "\\angle A O B = \\angle B O A _ { 1 } + \\angle A _ { 1 } O A\n", "\\angle A O B = \\angle B O A _1 + \\angle A _1 O A\n" ]	The image shows a handwritten equation that reads "B^3 + A^4". The equation appears to be written in black ink on a white background. The letters "B" and "A" are capitalized, and the numbers "3" and "4" are written in superscript form to indicate exponentiation. The equation is written in a cursive style, with the letters connected to each other. The overall appearance of the image suggests that it may have been written by hand with a pen or marker.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	910	[ "x = \\frac { 1 7 } { 5 }\n" ]	The image is a close-up of a blurred text that reads "K2". The text appears to be in a serif font and is slightly tilted to the right. The background is a solid light color, possibly white or cream. The overall effect is abstract and minimalistic.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	911	[ "2 S _ { 3 } = 5 S _ { 1 } + 2 S _ { 2 }\n", "2 S_3 = 5 S_1 + 2 S_2 \n" ]	The image appears to be a close-up of a handwritten letter or symbol. The writing is done in black ink on a white background. The style of the writing is cursive, with flowing lines and loops. The letter or symbol is not immediately recognizable due to the close-up nature of the image.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	912	[ "x = \\frac { 3 } { 1 6 } \\div \\frac { 1 } { 8 }\n" ]	The image shows a handwritten mathematical expression on a white surface. The expression is "3 - √7T/16", which represents the subtraction of the square root of 7 times T, all divided by 16, from the number 3. The handwriting is in black ink and appears to be done with a pen or marker. The background is plain white, with no other visible elements or distractions.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	913	[ "( 3 x + y ) ( 3 x - y ) = 0\n" ]	The image shows a piece of paper with handwritten text. The text appears to be a mathematical expression or equation, as indicated by the use of parentheses and the number "3". The handwriting is in black ink and the paper has a white background. The text is written in a cursive style, with the letters connected to each other. The overall appearance of the image suggests that it may have been taken in a classroom or study setting.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	914	[ "( x - 1 ) + \\frac { 2 } { x - 1 } = \\frac { a ^ { 2 } - 2 a + 1 } { a - 1 } + \\frac { 2 } { a - 1 }\n", "( x - 1 ) + \\frac { 2 } { x - 1 } = \\frac { a^2 - 2 a + 1 } { a - 1 } + \\frac { 2 } { a - 1 }\n" ]	The image appears to be a handwritten equation or mathematical expression. It consists of the letter "O" written in a cursive style, followed by a dash and then the symbol for a square root. The square root symbol is incomplete and does not enclose any numbers or variables. The handwriting is done with a thin, continuous line that suggests it was written with a pen or marker. The background is plain white, which contrasts with the dark color of the ink used for writing.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	915	[ "\\lambda \\geq [ \\frac { 2 n } { n ^ { 2 } + 5 n + x } ] \\max\n", "\\lambda \\geq [ \\frac { 2 n } { n^2 + 5 n + x } ] \\max\n" ]	The image shows a handwritten mathematical expression on a piece of paper. The expression is a fraction with the numerator "2" and the denominator "h^2 + t^2". The handwriting appears to be in black ink, and the paper has a grid pattern in the background.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	917	[ "\\sqrt { 1 + \\frac { 2 4 } { 2 5 } } = \\frac { 7 } { 5 }\n" ]	The image shows a handwritten calculation on a piece of paper. The calculation is for the subtraction of 24 from 25, which results in 1. The numbers are written in black ink and the paper has lines on it, suggesting it may be a notebook or lined paper. The handwriting appears to be neat and legible.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	918	[ "9 . 3 \\times 5 . 6 = 5 2 . 0 8 ( m ^ { 2 } )\n", "9 . 3 \\times 5 . 6 = 5 2 . 0 8 ( m^2 )\n" ]	The image shows a handwritten equation with the symbol "≥" followed by the number "5". The equation is written in black ink on a white background. The handwriting appears to be in cursive style, with the letters flowing together. The equation suggests that the value being represented must be greater than or equal to 5.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	919	[ "\\frac { 1 } { 2 } m + 3 = 1\n" ]	The image shows a handwritten equation that reads "x^2 + 3". The equation is written in black ink on a white background. The handwriting appears to be in cursive style, with the letters flowing together. The equation suggests that it is a quadratic equation with a constant term of 3.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	920	[ "b = \\sqrt { 3 }\n", "b = \\sqrt3 \n" ]	The image shows a mathematical equation written in black ink on a white surface. The equation is "√3 - 1/√3". The square root symbol (√) is used twice in the equation, once before the number 3 and once before the fraction 1/√3. The fraction 1/√3 is written with the number 1 above the square root symbol and the number 3 below it. The equation appears to be a simplified form of a more complex expression involving square roots.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	923	[ "9 0 \\div 3 . 1 4 \\approx 2 8 . 7 ( c m )\n" ]	The image shows a black and white abstract design that resembles a flowing river or a curved line. The line is thick and has a smooth, wavy texture that gives the impression of movement. The background is plain and light-colored, which contrasts with the dark color of the line. The overall effect is one of simplicity and elegance.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	924	[ "a + b = - c\n" ]	The image appears to be a close-up of a surface with two black vertical lines. The background is a light color, possibly white or cream, and there are some darker spots or marks scattered around the area. The texture of the surface is not clear due to the close-up nature of the photo. The black lines are straight and have a uniform width. There is no additional context provided in the image to determine the exact nature of the surface or the purpose of the lines.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	926	[ "\\frac { 1 } { 5 } \\times \\frac { 2 4 } { 5 } = 0 . 9 6\n" ]	The image shows a handwritten equation on a white surface. The equation is "22 ÷ 5 = 4.4". The numbers and the division symbol are written in black marker, with the equals sign and the decimal point slightly smudged. The handwriting is slightly messy, with the numbers not perfectly straight or aligned. The background of the image is white, with some creases and folds visible.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	927	[ "y = \\frac { 1 } { 3 } x + 2\n" ]	The image shows a handwritten mathematical equation on a piece of paper. The equation appears to be a fraction, with the numerator being a single vertical line and the denominator being the number 2 written in cursive script. Below the fraction, there is the letter X written in uppercase. The handwriting is done in black ink and the paper has a light beige color. The equation seems to be incomplete or possibly a part of a larger mathematical expression.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	933	[ "5 0 0 \\sqrt { 3 } + 5 0 0\n", "5 0 0 \\sqrt3 + 5 0 0\n" ]	The image shows a piece of paper with handwritten mathematical equations. The equations appear to be related to trigonometry, specifically involving the sine function. The handwriting is in black ink and the paper has a white background. The equations are written in a vertical column and take up most of the space on the paper.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	935	[ "\\cos \\alpha = - \\frac { 3 } { 5 }\n" ]	The image appears to be a low-resolution, grayscale image with some text or symbols. The text is not clear enough to read, but it seems to consist of a few letters or characters that are not in focus. The background is a solid gray color, and the overall quality of the image is poor.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	936	[ "( 2 ) m g R = \\frac { 1 } { 2 } m V B ^ { 2 } - \\frac { 1 } { 2 } m V D ^ { 2 }\n", "( 2 ) m g R = \\frac { 1 } { 2 } m V B ^2 - \\frac { 1 } { 2 } m V D^2\n" ]	The image shows a handwritten mathematical expression on a white surface. The expression appears to be a fraction with the numerator "l" (which could be a lowercase "L" or the letter "I") and the denominator "2m". The handwriting is in black ink and has a casual, informal style. The background is plain white, and there are no other objects or elements visible in the image.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	939	[ "\\Delta A D E \\cong \\Delta C B E ( S A S )\n" ]	The image shows a handwritten text that appears to be in cursive writing. The letters are connected and flowing, with loops and curves. The writing is done in black ink on a white background. The text is not entirely clear due to the angle and quality of the image, but it seems to resemble the word "cursive" or a similar combination of letters. The style of the handwriting suggests an attempt at a formal or decorative script.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	941	[ "4 x ^ { 2 } + ( 4 n - 4 ) x + n ^ { 2 } = 0\n", "4 x ^2 + ( 4 n - 4 ) x + n ^2 = 0\n" ]	The image shows a handwritten mathematical expression with the symbols "∂" and "μ" written in black ink on a white background. The "∂" symbol is commonly used to represent a partial derivative in calculus, while the "μ" symbol can represent various things depending on the context, such as the Greek letter mu or the symbol for the magnetic permeability constant in physics. The expression appears to be part of a larger equation or calculation, but only these two symbols are visible in the image.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	942	[ "[ \\arccos \\frac { 1 } { 4 } , \\pi ]\n" ]	The image shows a handwritten number "105" in red ink on a white background. The numbers are written in cursive style, with the "1" being larger and more prominent than the "0" and "5". The "0" is slightly curved and the "5" has a long tail. The handwriting appears to be done with a marker or pen.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	945	[ "x = - \\frac { 3 } { 7 }\n" ]	The image appears to be a close-up of a surface with several small, dark spots or marks scattered across it. The background is a light beige color, and the spots are irregular in shape and size. It is difficult to determine what the surface is made of or what the spots represent without more context.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	948	[ "\\cos c = \\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b }\n", "\\cos c = \\frac { a ^2 + b ^2 - c^2 } { 2 a b }\n" ]	The image shows a handwritten mathematical equation on a piece of paper. The equation appears to be a quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants. The handwriting is in black ink and the paper has a white background. The equation is written in a cursive style, with the letters connected to each other. The equation is centered on the paper and takes up most of the space. There are no other elements or objects in the image.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	949	[ "1 4 . a / / c\n" ]	The image shows a simple, curved line that appears to be hand-drawn. The line has a smooth, flowing shape and is slightly uneven, giving it a casual and informal look. The background of the image is plain white, which makes the line stand out more prominently. There are no other elements or objects in the image, just the single curved line.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	951	[ "3 \\sqrt { - 6 4 } = - 4\n" ]	The image shows a handwritten equation on a white background. The equation is written in black ink and reads "b^4 = b^6". The handwriting is cursive and the letters are connected, giving the equation a flowing appearance. The equation itself suggests that the fourth power of a variable "b" is equal to the sixth power of the same variable.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	952	[ "1 > P > \\frac { 1 } { 2 }\n" ]	The image shows a handwritten symbol that appears to be a combination of the letter "P" and the number "7". The "P" is written in a cursive style with a loop at the top, and the "7" is written in a vertical line with a diagonal line extending from the top right corner. The handwriting is done in black ink on a white background.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	955	[ "\\rho = \\frac { m } { V } = \\frac { 2 k g } { 2 . 5 \\times 1 0 ^ { - 3 } m ^ { 3 } } = 8 0 0 k g / m ^ { 3 }\n", "\\rho = \\frac { m } { V } = \\frac { 2 k g } { 2 . 5 \\times 1 0 ^ { - 3 } m ^3 } = 8 0 0 k g / m^3\n" ]	The image shows a handwritten equation on a white background. The equation is divided into two parts by a horizontal line. The top part of the equation has a single letter "m" written in black ink. The bottom part of the equation has the number "-3" written in black ink, followed by the letter "m" written in black ink. The equation appears to be incomplete and may be part of a larger mathematical problem or calculation.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	957	[ "\\angle B C D = 1 2 0 ^ { \\circ }\n", "\\angle B C D = 1 2 0 ^ \\circ \n" ]	The image shows a single letter "D" in a bold, serif font. The letter is black and has a slight shadow effect, giving it a three-dimensional appearance. The background is a light blue color.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	958	[ "\\angle A B D = 9 0 ^ { \\circ } - 6 0 ^ { \\circ } = 3 0 ^ { \\circ }\n", "\\angle A B D = 9 0 ^ \\circ - 6 0 ^\\circ = 3 0 ^ \\circ \n" ]	The image shows a handwritten mathematical expression, specifically the square root of 100. The numbers are written in black ink on a white background. The square root symbol is represented by a curved line with a small horizontal line at the top, indicating that the number inside the root should be squared to find its value. The number 100 is written underneath the root symbol, with the two digits separated by a small space. The handwriting appears to be neat and legible, with consistent spacing and alignment of the numbers.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	959	[ "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n", "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ \\circ - 3 0 ^ \\circ ) = 7 5 ^ \\circ\n" ]	The image shows a handwritten mathematical equation on a piece of paper. The equation is a fraction with the number 1 as the numerator and the square of 2 (2^2) as the denominator. The handwriting appears to be in black ink, and the paper has a white background with lines for writing. The equation is centered on the paper, and there are no other visible elements in the image.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	960	[ "P ( 1 , - \\frac { 3 } { 2 } ) \\vert \\overrightarrow { F P } \\vert = \\frac { 3 } { 2 }\n" ]	The image shows a handwritten equation on a white piece of paper. The equation is written in blue ink and appears to be a mathematical expression, possibly involving variables and exponents. The handwriting is somewhat messy and the equation is not fully legible due to the quality of the image.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	962	[ "x _ { 3 } = - 2 + \\sqrt { 1 0 }\n", "x_3 = - 2 + \\sqrt { 1 0 }\n" ]	The image shows a handwritten mathematical inequality. The inequality is written in black ink on a white background. The equation reads "x^2 > 2". This means that the value of x squared must be greater than 2 for the inequality to hold true. The handwriting appears to be neat and legible, with clear distinction between the variables and numbers.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	964	[ "x - \\frac { 1 } { x } = \\frac { 8 } { 3 }\n" ]	The image shows a black and white cross with a vertical line intersected by a shorter horizontal line. The cross appears to be hand-drawn with uneven lines and a rough texture. The background is plain and unadorned, allowing the cross to be the focal point of the image.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	969	[ "\\angle G O B + \\angle E O G + \\angle A O E = 1 8 0 ^ { \\circ }\n", "\\angle G O B + \\angle E O G + \\angle A O E = 1 8 0^\\circ \n" ]	The image shows the word "DOG" written in black ink on a white background. The letters are capitalized and appear to be hand-written with a brush or marker, giving them a slightly uneven and organic look. The letters are spaced closely together, with the "D" and "G" being slightly larger than the "O". The overall appearance of the image is simple and minimalistic, with the focus being on the word itself rather than any additional design elements.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	970	[ "x _ { 1 } = 0\n", "x _ 1 = 0\n" ]	The image shows a piece of fabric with two black lines drawn on it. The lines are parallel and evenly spaced, creating a sense of symmetry and balance in the design. The fabric appears to be a solid color, possibly white or light gray, which contrasts with the black lines and makes them stand out. The overall impression is one of simplicity and elegance.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	972	[ "y = \\frac { 3 } { 2 }\n" ]	The image shows a close-up of a handwritten equation. The equation appears to be "i + i = 2i". The handwriting is in black ink on a white background. The letters and numbers are written in a cursive style, with the "i" being capitalized at the beginning of each instance. The equation suggests a basic principle of algebra, where adding two identical terms results in twice the original term.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	973	[ "0 . 3 x + 0 . 7 x + 0 . 2 8 = - 0 . 4 x\n" ]	The image shows a handwritten equation on a piece of paper. The equation is "x^2 + x + 0". The handwriting is in black ink and the paper has blue lines. The equation appears to be a quadratic equation, which is commonly used in algebra to represent a parabola.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	974	[ "( \\frac { 2 } { 3 } ) ^ { 2 } \\cdot \\frac { 1 } { 3 } = \\frac { 4 } { 2 7 }\n", "( \\frac { 2 } { 3 } )^2 \\cdot \\frac { 1 } { 3 } = \\frac { 4 } { 2 7 }\n" ]	The image shows a piece of paper with handwritten mathematical equations. The writing is in black ink and appears to be done with a pen or marker. The equations include numbers, fractions, and possibly some algebraic symbols, although the specific details of the equations are not clearly visible due to the angle and quality of the photograph. The paper has a white background and there are no other objects or texts present in the image.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	976	[ "\\frac { 9 } { 1 0 } = \\frac { 2 7 } { 3 0 }\n" ]	The image shows a mathematical equation written in black ink on a beige background. The equation is "x^2 = 3". This represents the equation of a parabola with a vertex at the origin (0,0) and a horizontal axis of symmetry. The parabola opens upwards and has a width of 3 units.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	978	[ "m > \\frac { 2 } { 3 }\n" ]	The image shows a handwritten mathematical equation on a white piece of paper. The equation appears to be a quadratic equation, with the variable "x" raised to the power of 2. There are also two other terms in the equation, one with the variable "x" and another constant term. The equation is written in black ink, with the variable "x" and the constant term underlined in red ink. The handwriting is slightly messy, with some of the letters and numbers overlapping each other.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	980	[ "1 0 \\times 1 0 \\times 2 0 + 1 0 \\times 3 0 \\times 2 0 = 8 0 0 0 ( c m ^ { 3 } )\n", "1 0 \\times 1 0 \\times 2 0 + 1 0 \\times 3 0 \\times 2 0 = 8 0 0 0 ( c m^3 )\n" ]	The image shows a handwritten equation that appears to be a multiplication problem. The equation is written in black ink on a white background. The numbers are slightly smudged and the handwriting is not very neat, making it difficult to read the exact values. The equation seems to involve two numbers being multiplied together, with the result written below them. The overall appearance of the image suggests that it may have been written quickly or by someone with poor handwriting skills.
HME100k	middle	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	981	[ "4 x = 4 \\times 1 7 . 2 = 6 8 . 8\n" ]	The image shows the number 17 written in black ink on a white background. The number is slightly tilted to the right and has a handwritten appearance with uneven lines and edges. There are no other elements or objects in the image, just the number 17.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	983	[ "x > \\frac { 3 } { 2 }\n" ]	The image shows a handwritten mathematical inequality. The inequality is written in black ink on a white background. The left side of the inequality contains a symbol that resembles a stylized "3" with a horizontal line through it, and above the line, there is a smaller "3" with a dot above it. The right side of the inequality has a similar symbol, but the horizontal line is replaced by a curved line resembling a sine wave, and the smaller "3" with a dot is replaced by a larger "3" without a dot. The inequality sign, which is the greater-than symbol (">"), is placed between the two sides of the inequality. The overall appearance of the image suggests that it may be a student's notes or solutions to a math problem.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	985	[ "- \\frac { 1 } { 2 }\n" ]	The image appears to be a handwritten note or signature. It consists of two vertical lines, one above the other, with the top line being slightly longer than the bottom line. The lines are thick and have a rough, uneven edge, suggesting that they were drawn quickly or with a heavy hand. The background is a plain, light color, providing a stark contrast to the dark lines. Overall, the image has a simple yet bold appearance.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	986	[ "O D \\bot A B\n" ]	The image is a close-up of a blurry object that appears to be a black letter "L" with a white background. The letter is slightly tilted to the right and has a three-dimensional effect, giving it depth and dimension. The edges of the letter are sharp and defined, while the center is more indistinct and out of focus. The overall appearance of the image is abstract and artistic, with a monochromatic color scheme.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	989	[ "\\frac { 3 } { 2 } y - y ^ { 2 } - \\frac { 1 } { 2 } = 0\n", "\\frac { 3 } { 2 } y - y ^2 - \\frac { 1 } { 2 } = 0\n" ]	The image shows a handwritten equation or expression that appears to be written in cursive script. The text is somewhat blurred and the resolution is low, making it difficult to read the exact details of the equation. It seems to contain mathematical symbols such as integrals or summations, but the specifics are not clear due to the quality of the image.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	991	[ "c \\% = \\frac { 5 . 3 g } { 2 0 g } \\times 1 0 0 \\% = 2 6 . 5 \\%\n" ]	The image shows a blurry text that appears to be "x100" written in a sans-serif font. The text is white with a slight shadow effect, giving it a slightly three-dimensional appearance. The background is a solid light gray color. The overall style of the image is minimalistic and modern.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	992	[ "4 = \\frac { 4 \\times 3 } { 1 \\times 3 } = \\frac { 1 2 } { 3 }\n" ]	The image shows a handwritten mathematical equation. The equation is written in blue ink on a white background. The equation appears to be a fraction, with the numerator being "h^4x^3" and the denominator being "h^2x^3". The equation is written in a cursive style, with the letters flowing together. The equation is centered in the image, with equal amounts of white space above and below it. The equation is the only element in the image, with no other objects or text present.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	993	[ "f ( - 1 ) \\cdot f ( 1 ) \\leq 0\n" ]	The image shows a handwritten equation in pink ink on a white background. The equation appears to be a fraction with the numerator being a single letter "f" and the denominator being a combination of the letters "f" and "k". The handwriting is slightly messy, with the lines of the equation not being perfectly straight. The overall appearance of the image is simple and minimalistic.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	994	[ "\\frac { 1 } { x + y } = \\frac { 1 } { 2 }\n" ]	The image shows a handwritten equation on a white surface. The equation is written in black ink and appears to be a mathematical expression involving the variable "y". The handwriting is somewhat messy, with some of the letters and numbers overlapping or not fully formed. The equation itself is not fully visible, as only the right side of it is shown in the image.
HME100k	difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	997	[ "x > - \\frac { 5 } { 2 }\n" ]	The image shows a handwritten mathematical expression on a white piece of paper. The expression consists of two symbols: a greater than or equal to sign (≥) and a less than or equal to sign (≤). The symbols are written in black ink and appear to be drawn with a pen or marker. The paper has a smooth texture and is free of any other markings or text. The overall appearance of the image is simple and focused on the mathematical symbols.
HME100k	very_difficult	Please write out the expression of the formula in the image using LaTeX format.	Handwritten Mathematical Expression Recognition	998	[ "\\angle B A C = \\frac { 1 } { 2 } \\angle B O C\n" ]	The image shows a handwritten mathematical equation on a white surface. The equation is written in black ink and appears to be a ratio or fraction, with the numerator being "1" and the denominator being a complex expression involving the square root of "L^2". The handwriting is somewhat messy and the equation is not fully legible due to the angle and quality of the image.

POIE

difficult

what is the value for Calories/Energy of per serving? Answer this question using the text in the image directly.

Key Information Extraction

897

[ "858", "206" ]

The image is a table comparing the nutritional values of two different types of food. The first column lists the type of nutrient, such as energy (kcal), fat, saturates, carbohydrates, sugars, and protein. The second column shows the per 100g values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The third column shows the per burger values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The fourth column shows the % as per instructions values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The fifth column shows the per 100g values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food has higher values for carbohydrates and sugars. The sixth column shows the per burger values for each nutrient, with the first food having higher values for energy, fat, saturates, and protein, while the second food

POIE

difficult

what is the value for Sodium of per 100g/ml? Answer this question using the text in the image directly.

Key Information Extraction

899

[ "15mg", "15 mg" ]

The image is a nutrition label for a food product. It lists the calories per serving, which is 150 calories, and the percentage of daily value (% DV) for various nutrients. The nutrients listed include total fat, saturated fat, trans fat, cholesterol, sodium, total carbohydrates, dietary fiber, total sugars, and protein. Each nutrient has a corresponding amount per serving and a percentage of daily value based on a 2,000 calorie diet. The label also includes the amount of monounsaturated fat and polyunsaturated fat per serving.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

900

[ "y _ { 2 } = - 1\n", "y_2 = - 1\n" ]

The image shows a handwritten note with the letters "Y" and "E" written in black ink on a white background. The writing appears to be done with a pen or marker, and the letters are written in a cursive style. The "Y" is larger and more prominent than the "E," and both letters are connected at the top. The handwriting is slightly slanted to the right, giving it a dynamic and informal appearance.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

901

[ "x _ { 1 } = \\frac { - 2 + 2 \\sqrt { 2 } } { 2 }\n", "x_1 = \\frac { - 2 + 2 \\sqrt { 2 } } { 2 }\n" ]

The image shows a mathematical expression written in black ink on a white background. The expression appears to be a fraction with a numerator and a denominator. The numerator contains the number 3 and a plus sign, followed by another number which is not fully visible. The denominator contains the number 1. The overall expression seems to represent a simple algebraic fraction.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

902

[ "V = \\frac { F } { \\rho } = \\frac { 7 . 6 N } { 0 . 8 \\times 1 0 ^ { 3 } k g / m ^ { 2 } \\times 1 0 N / k g } = 0 . 9 5 \\times 1 0 ^ { - 3 } m ^ { 3 }\n", "V = \\frac { F } { \\rho } = \\frac { 7 . 6 N } { 0 . 8 \\times 1 0 ^3 k g / m^2 \\times 1 0 N / k g } = 0 . 9 5 \\times 1 0 ^ { - 3 } m^3\n" ]

The image shows a piece of paper with handwritten text in black ink. The text appears to be a mathematical equation or expression, as it includes the symbols "x" and "/". There is also a line drawn through the text, indicating that it may have been crossed out or marked for correction. The background of the paper is white, and there are grid lines visible, suggesting that the paper may be from a notebook or graph paper.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

904

[ "I _ { 2 } = \\frac { u } { R _ { 2 } } = \\frac { 6 V } { 1 0 \\Omega } = 0 . 6 A\n", "I _2= \\frac { u } { R_2} = \\frac { 6 V } { 1 0 \\Omega } = 0 . 6 A\n" ]

The image shows a handwritten mathematical equation. The equation is written in black ink on a white background. The equation reads "-2/6V". The number "-2" is written at the top left corner of the equation, and the fraction "1/6V" is written at the bottom right corner. The equation appears to be a ratio or proportion involving the number "-2" and the volume "6V". The handwriting is clear and legible, with the numbers and symbols properly spaced and aligned.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

905

[ "- 6 x = \\frac { 2 } { 3 } - 3 + 4\n" ]

The image shows a mathematical equation written in black ink on a white background. The equation is a fraction with the number 2 as the numerator and the number 3 as the denominator, separated by a horizontal line. The equation is centered in the image and takes up most of the space. The numbers are written in a simple, clear font that is easy to read. The overall appearance of the image is clean and minimalistic, with no additional decorations or embellishments.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

906

[ "\\frac { 6 . 8 } { x } = \\frac { 1 . 7 } { 4 }\n" ]

The image shows a handwritten mathematical equation on a white surface. The equation appears to be a fraction with the numerator being "1" and the denominator being "x^2 - 7x + 8". The handwriting is in black ink, and the equation is written in a cursive style. The background of the image is plain white, and there are no other objects or elements present in the image.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

909

[ "\\angle A O B = \\angle B O A _ { 1 } + \\angle A _ { 1 } O A\n", "\\angle A O B = \\angle B O A _1 + \\angle A _1 O A\n" ]

The image shows a handwritten equation that reads "B^3 + A^4". The equation appears to be written in black ink on a white background. The letters "B" and "A" are capitalized, and the numbers "3" and "4" are written in superscript form to indicate exponentiation. The equation is written in a cursive style, with the letters connected to each other. The overall appearance of the image suggests that it may have been written by hand with a pen or marker.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

910

[ "x = \\frac { 1 7 } { 5 }\n" ]

The image is a close-up of a blurred text that reads "K2". The text appears to be in a serif font and is slightly tilted to the right. The background is a solid light color, possibly white or cream. The overall effect is abstract and minimalistic.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

911

[ "2 S _ { 3 } = 5 S _ { 1 } + 2 S _ { 2 }\n", "2 S_3 = 5 S_1 + 2 S_2 \n" ]

The image appears to be a close-up of a handwritten letter or symbol. The writing is done in black ink on a white background. The style of the writing is cursive, with flowing lines and loops. The letter or symbol is not immediately recognizable due to the close-up nature of the image.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

912

[ "x = \\frac { 3 } { 1 6 } \\div \\frac { 1 } { 8 }\n" ]

The image shows a handwritten mathematical expression on a white surface. The expression is "3 - √7T/16", which represents the subtraction of the square root of 7 times T, all divided by 16, from the number 3. The handwriting is in black ink and appears to be done with a pen or marker. The background is plain white, with no other visible elements or distractions.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

913

[ "( 3 x + y ) ( 3 x - y ) = 0\n" ]

The image shows a piece of paper with handwritten text. The text appears to be a mathematical expression or equation, as indicated by the use of parentheses and the number "3". The handwriting is in black ink and the paper has a white background. The text is written in a cursive style, with the letters connected to each other. The overall appearance of the image suggests that it may have been taken in a classroom or study setting.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

914

[ "( x - 1 ) + \\frac { 2 } { x - 1 } = \\frac { a ^ { 2 } - 2 a + 1 } { a - 1 } + \\frac { 2 } { a - 1 }\n", "( x - 1 ) + \\frac { 2 } { x - 1 } = \\frac { a^2 - 2 a + 1 } { a - 1 } + \\frac { 2 } { a - 1 }\n" ]

The image appears to be a handwritten equation or mathematical expression. It consists of the letter "O" written in a cursive style, followed by a dash and then the symbol for a square root. The square root symbol is incomplete and does not enclose any numbers or variables. The handwriting is done with a thin, continuous line that suggests it was written with a pen or marker. The background is plain white, which contrasts with the dark color of the ink used for writing.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

915

[ "\\lambda \\geq [ \\frac { 2 n } { n ^ { 2 } + 5 n + x } ] \\max\n", "\\lambda \\geq [ \\frac { 2 n } { n^2 + 5 n + x } ] \\max\n" ]

The image shows a handwritten mathematical expression on a piece of paper. The expression is a fraction with the numerator "2" and the denominator "h^2 + t^2". The handwriting appears to be in black ink, and the paper has a grid pattern in the background.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

917

[ "\\sqrt { 1 + \\frac { 2 4 } { 2 5 } } = \\frac { 7 } { 5 }\n" ]

The image shows a handwritten calculation on a piece of paper. The calculation is for the subtraction of 24 from 25, which results in 1. The numbers are written in black ink and the paper has lines on it, suggesting it may be a notebook or lined paper. The handwriting appears to be neat and legible.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

918

[ "9 . 3 \\times 5 . 6 = 5 2 . 0 8 ( m ^ { 2 } )\n", "9 . 3 \\times 5 . 6 = 5 2 . 0 8 ( m^2 )\n" ]

The image shows a handwritten equation with the symbol "≥" followed by the number "5". The equation is written in black ink on a white background. The handwriting appears to be in cursive style, with the letters flowing together. The equation suggests that the value being represented must be greater than or equal to 5.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

919

[ "\\frac { 1 } { 2 } m + 3 = 1\n" ]

The image shows a handwritten equation that reads "x^2 + 3". The equation is written in black ink on a white background. The handwriting appears to be in cursive style, with the letters flowing together. The equation suggests that it is a quadratic equation with a constant term of 3.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

920

[ "b = \\sqrt { 3 }\n", "b = \\sqrt3 \n" ]

The image shows a mathematical equation written in black ink on a white surface. The equation is "√3 - 1/√3". The square root symbol (√) is used twice in the equation, once before the number 3 and once before the fraction 1/√3. The fraction 1/√3 is written with the number 1 above the square root symbol and the number 3 below it. The equation appears to be a simplified form of a more complex expression involving square roots.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

923

[ "9 0 \\div 3 . 1 4 \\approx 2 8 . 7 ( c m )\n" ]

The image shows a black and white abstract design that resembles a flowing river or a curved line. The line is thick and has a smooth, wavy texture that gives the impression of movement. The background is plain and light-colored, which contrasts with the dark color of the line. The overall effect is one of simplicity and elegance.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

924

[ "a + b = - c\n" ]

The image appears to be a close-up of a surface with two black vertical lines. The background is a light color, possibly white or cream, and there are some darker spots or marks scattered around the area. The texture of the surface is not clear due to the close-up nature of the photo. The black lines are straight and have a uniform width. There is no additional context provided in the image to determine the exact nature of the surface or the purpose of the lines.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

926

[ "\\frac { 1 } { 5 } \\times \\frac { 2 4 } { 5 } = 0 . 9 6\n" ]

The image shows a handwritten equation on a white surface. The equation is "22 ÷ 5 = 4.4". The numbers and the division symbol are written in black marker, with the equals sign and the decimal point slightly smudged. The handwriting is slightly messy, with the numbers not perfectly straight or aligned. The background of the image is white, with some creases and folds visible.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

927

[ "y = \\frac { 1 } { 3 } x + 2\n" ]

The image shows a handwritten mathematical equation on a piece of paper. The equation appears to be a fraction, with the numerator being a single vertical line and the denominator being the number 2 written in cursive script. Below the fraction, there is the letter X written in uppercase. The handwriting is done in black ink and the paper has a light beige color. The equation seems to be incomplete or possibly a part of a larger mathematical expression.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

933

[ "5 0 0 \\sqrt { 3 } + 5 0 0\n", "5 0 0 \\sqrt3 + 5 0 0\n" ]

The image shows a piece of paper with handwritten mathematical equations. The equations appear to be related to trigonometry, specifically involving the sine function. The handwriting is in black ink and the paper has a white background. The equations are written in a vertical column and take up most of the space on the paper.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

935

[ "\\cos \\alpha = - \\frac { 3 } { 5 }\n" ]

The image appears to be a low-resolution, grayscale image with some text or symbols. The text is not clear enough to read, but it seems to consist of a few letters or characters that are not in focus. The background is a solid gray color, and the overall quality of the image is poor.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

936

[ "( 2 ) m g R = \\frac { 1 } { 2 } m V B ^ { 2 } - \\frac { 1 } { 2 } m V D ^ { 2 }\n", "( 2 ) m g R = \\frac { 1 } { 2 } m V B ^2 - \\frac { 1 } { 2 } m V D^2\n" ]

The image shows a handwritten mathematical expression on a white surface. The expression appears to be a fraction with the numerator "l" (which could be a lowercase "L" or the letter "I") and the denominator "2m". The handwriting is in black ink and has a casual, informal style. The background is plain white, and there are no other objects or elements visible in the image.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

939

[ "\\Delta A D E \\cong \\Delta C B E ( S A S )\n" ]

The image shows a handwritten text that appears to be in cursive writing. The letters are connected and flowing, with loops and curves. The writing is done in black ink on a white background. The text is not entirely clear due to the angle and quality of the image, but it seems to resemble the word "cursive" or a similar combination of letters. The style of the handwriting suggests an attempt at a formal or decorative script.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

941

[ "4 x ^ { 2 } + ( 4 n - 4 ) x + n ^ { 2 } = 0\n", "4 x ^2 + ( 4 n - 4 ) x + n ^2 = 0\n" ]

The image shows a handwritten mathematical expression with the symbols "∂" and "μ" written in black ink on a white background. The "∂" symbol is commonly used to represent a partial derivative in calculus, while the "μ" symbol can represent various things depending on the context, such as the Greek letter mu or the symbol for the magnetic permeability constant in physics. The expression appears to be part of a larger equation or calculation, but only these two symbols are visible in the image.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

942

[ "[ \\arccos \\frac { 1 } { 4 } , \\pi ]\n" ]

The image shows a handwritten number "105" in red ink on a white background. The numbers are written in cursive style, with the "1" being larger and more prominent than the "0" and "5". The "0" is slightly curved and the "5" has a long tail. The handwriting appears to be done with a marker or pen.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

945

[ "x = - \\frac { 3 } { 7 }\n" ]

The image appears to be a close-up of a surface with several small, dark spots or marks scattered across it. The background is a light beige color, and the spots are irregular in shape and size. It is difficult to determine what the surface is made of or what the spots represent without more context.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

948

[ "\\cos c = \\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b }\n", "\\cos c = \\frac { a ^2 + b ^2 - c^2 } { 2 a b }\n" ]

The image shows a handwritten mathematical equation on a piece of paper. The equation appears to be a quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants. The handwriting is in black ink and the paper has a white background. The equation is written in a cursive style, with the letters connected to each other. The equation is centered on the paper and takes up most of the space. There are no other elements or objects in the image.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

949

[ "1 4 . a / / c\n" ]

The image shows a simple, curved line that appears to be hand-drawn. The line has a smooth, flowing shape and is slightly uneven, giving it a casual and informal look. The background of the image is plain white, which makes the line stand out more prominently. There are no other elements or objects in the image, just the single curved line.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

951

[ "3 \\sqrt { - 6 4 } = - 4\n" ]

The image shows a handwritten equation on a white background. The equation is written in black ink and reads "b^4 = b^6". The handwriting is cursive and the letters are connected, giving the equation a flowing appearance. The equation itself suggests that the fourth power of a variable "b" is equal to the sixth power of the same variable.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

952

[ "1 > P > \\frac { 1 } { 2 }\n" ]

The image shows a handwritten symbol that appears to be a combination of the letter "P" and the number "7". The "P" is written in a cursive style with a loop at the top, and the "7" is written in a vertical line with a diagonal line extending from the top right corner. The handwriting is done in black ink on a white background.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

955

[ "\\rho = \\frac { m } { V } = \\frac { 2 k g } { 2 . 5 \\times 1 0 ^ { - 3 } m ^ { 3 } } = 8 0 0 k g / m ^ { 3 }\n", "\\rho = \\frac { m } { V } = \\frac { 2 k g } { 2 . 5 \\times 1 0 ^ { - 3 } m ^3 } = 8 0 0 k g / m^3\n" ]

The image shows a handwritten equation on a white background. The equation is divided into two parts by a horizontal line. The top part of the equation has a single letter "m" written in black ink. The bottom part of the equation has the number "-3" written in black ink, followed by the letter "m" written in black ink. The equation appears to be incomplete and may be part of a larger mathematical problem or calculation.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

957

[ "\\angle B C D = 1 2 0 ^ { \\circ }\n", "\\angle B C D = 1 2 0 ^ \\circ \n" ]

The image shows a single letter "D" in a bold, serif font. The letter is black and has a slight shadow effect, giving it a three-dimensional appearance. The background is a light blue color.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

958

[ "\\angle A B D = 9 0 ^ { \\circ } - 6 0 ^ { \\circ } = 3 0 ^ { \\circ }\n", "\\angle A B D = 9 0 ^ \\circ - 6 0 ^\\circ = 3 0 ^ \\circ \n" ]

The image shows a handwritten mathematical expression, specifically the square root of 100. The numbers are written in black ink on a white background. The square root symbol is represented by a curved line with a small horizontal line at the top, indicating that the number inside the root should be squared to find its value. The number 100 is written underneath the root symbol, with the two digits separated by a small space. The handwriting appears to be neat and legible, with consistent spacing and alignment of the numbers.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

959

[ "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ { \\circ } - 3 0 ^ { \\circ } ) = 7 5 ^ { \\circ }\n", "\\angle B D E = \\angle B E D = \\frac { 1 } { 2 } ( 1 8 0 ^ \\circ - 3 0 ^ \\circ ) = 7 5 ^ \\circ\n" ]

The image shows a handwritten mathematical equation on a piece of paper. The equation is a fraction with the number 1 as the numerator and the square of 2 (2^2) as the denominator. The handwriting appears to be in black ink, and the paper has a white background with lines for writing. The equation is centered on the paper, and there are no other visible elements in the image.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

960

[ "P ( 1 , - \\frac { 3 } { 2 } ) \\vert \\overrightarrow { F P } \\vert = \\frac { 3 } { 2 }\n" ]

The image shows a handwritten equation on a white piece of paper. The equation is written in blue ink and appears to be a mathematical expression, possibly involving variables and exponents. The handwriting is somewhat messy and the equation is not fully legible due to the quality of the image.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

962

[ "x _ { 3 } = - 2 + \\sqrt { 1 0 }\n", "x_3 = - 2 + \\sqrt { 1 0 }\n" ]

The image shows a handwritten mathematical inequality. The inequality is written in black ink on a white background. The equation reads "x^2 > 2". This means that the value of x squared must be greater than 2 for the inequality to hold true. The handwriting appears to be neat and legible, with clear distinction between the variables and numbers.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

964

[ "x - \\frac { 1 } { x } = \\frac { 8 } { 3 }\n" ]

The image shows a black and white cross with a vertical line intersected by a shorter horizontal line. The cross appears to be hand-drawn with uneven lines and a rough texture. The background is plain and unadorned, allowing the cross to be the focal point of the image.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

969

[ "\\angle G O B + \\angle E O G + \\angle A O E = 1 8 0 ^ { \\circ }\n", "\\angle G O B + \\angle E O G + \\angle A O E = 1 8 0^\\circ \n" ]

The image shows the word "DOG" written in black ink on a white background. The letters are capitalized and appear to be hand-written with a brush or marker, giving them a slightly uneven and organic look. The letters are spaced closely together, with the "D" and "G" being slightly larger than the "O". The overall appearance of the image is simple and minimalistic, with the focus being on the word itself rather than any additional design elements.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

970

[ "x _ { 1 } = 0\n", "x _ 1 = 0\n" ]

The image shows a piece of fabric with two black lines drawn on it. The lines are parallel and evenly spaced, creating a sense of symmetry and balance in the design. The fabric appears to be a solid color, possibly white or light gray, which contrasts with the black lines and makes them stand out. The overall impression is one of simplicity and elegance.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

972

[ "y = \\frac { 3 } { 2 }\n" ]

The image shows a close-up of a handwritten equation. The equation appears to be "i + i = 2i". The handwriting is in black ink on a white background. The letters and numbers are written in a cursive style, with the "i" being capitalized at the beginning of each instance. The equation suggests a basic principle of algebra, where adding two identical terms results in twice the original term.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

973

[ "0 . 3 x + 0 . 7 x + 0 . 2 8 = - 0 . 4 x\n" ]

The image shows a handwritten equation on a piece of paper. The equation is "x^2 + x + 0". The handwriting is in black ink and the paper has blue lines. The equation appears to be a quadratic equation, which is commonly used in algebra to represent a parabola.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

974

[ "( \\frac { 2 } { 3 } ) ^ { 2 } \\cdot \\frac { 1 } { 3 } = \\frac { 4 } { 2 7 }\n", "( \\frac { 2 } { 3 } )^2 \\cdot \\frac { 1 } { 3 } = \\frac { 4 } { 2 7 }\n" ]

The image shows a piece of paper with handwritten mathematical equations. The writing is in black ink and appears to be done with a pen or marker. The equations include numbers, fractions, and possibly some algebraic symbols, although the specific details of the equations are not clearly visible due to the angle and quality of the photograph. The paper has a white background and there are no other objects or texts present in the image.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

976

[ "\\frac { 9 } { 1 0 } = \\frac { 2 7 } { 3 0 }\n" ]

The image shows a mathematical equation written in black ink on a beige background. The equation is "x^2 = 3". This represents the equation of a parabola with a vertex at the origin (0,0) and a horizontal axis of symmetry. The parabola opens upwards and has a width of 3 units.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

978

[ "m > \\frac { 2 } { 3 }\n" ]

The image shows a handwritten mathematical equation on a white piece of paper. The equation appears to be a quadratic equation, with the variable "x" raised to the power of 2. There are also two other terms in the equation, one with the variable "x" and another constant term. The equation is written in black ink, with the variable "x" and the constant term underlined in red ink. The handwriting is slightly messy, with some of the letters and numbers overlapping each other.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

980

[ "1 0 \\times 1 0 \\times 2 0 + 1 0 \\times 3 0 \\times 2 0 = 8 0 0 0 ( c m ^ { 3 } )\n", "1 0 \\times 1 0 \\times 2 0 + 1 0 \\times 3 0 \\times 2 0 = 8 0 0 0 ( c m^3 )\n" ]

The image shows a handwritten equation that appears to be a multiplication problem. The equation is written in black ink on a white background. The numbers are slightly smudged and the handwriting is not very neat, making it difficult to read the exact values. The equation seems to involve two numbers being multiplied together, with the result written below them. The overall appearance of the image suggests that it may have been written quickly or by someone with poor handwriting skills.

HME100k

middle

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

981

[ "4 x = 4 \\times 1 7 . 2 = 6 8 . 8\n" ]

The image shows the number 17 written in black ink on a white background. The number is slightly tilted to the right and has a handwritten appearance with uneven lines and edges. There are no other elements or objects in the image, just the number 17.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

983

[ "x > \\frac { 3 } { 2 }\n" ]

The image shows a handwritten mathematical inequality. The inequality is written in black ink on a white background. The left side of the inequality contains a symbol that resembles a stylized "3" with a horizontal line through it, and above the line, there is a smaller "3" with a dot above it. The right side of the inequality has a similar symbol, but the horizontal line is replaced by a curved line resembling a sine wave, and the smaller "3" with a dot is replaced by a larger "3" without a dot. The inequality sign, which is the greater-than symbol (">"), is placed between the two sides of the inequality. The overall appearance of the image suggests that it may be a student's notes or solutions to a math problem.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

985

[ "- \\frac { 1 } { 2 }\n" ]

The image appears to be a handwritten note or signature. It consists of two vertical lines, one above the other, with the top line being slightly longer than the bottom line. The lines are thick and have a rough, uneven edge, suggesting that they were drawn quickly or with a heavy hand. The background is a plain, light color, providing a stark contrast to the dark lines. Overall, the image has a simple yet bold appearance.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

986

[ "O D \\bot A B\n" ]

The image is a close-up of a blurry object that appears to be a black letter "L" with a white background. The letter is slightly tilted to the right and has a three-dimensional effect, giving it depth and dimension. The edges of the letter are sharp and defined, while the center is more indistinct and out of focus. The overall appearance of the image is abstract and artistic, with a monochromatic color scheme.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

989

[ "\\frac { 3 } { 2 } y - y ^ { 2 } - \\frac { 1 } { 2 } = 0\n", "\\frac { 3 } { 2 } y - y ^2 - \\frac { 1 } { 2 } = 0\n" ]

The image shows a handwritten equation or expression that appears to be written in cursive script. The text is somewhat blurred and the resolution is low, making it difficult to read the exact details of the equation. It seems to contain mathematical symbols such as integrals or summations, but the specifics are not clear due to the quality of the image.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

991

[ "c \\% = \\frac { 5 . 3 g } { 2 0 g } \\times 1 0 0 \\% = 2 6 . 5 \\%\n" ]

The image shows a blurry text that appears to be "x100" written in a sans-serif font. The text is white with a slight shadow effect, giving it a slightly three-dimensional appearance. The background is a solid light gray color. The overall style of the image is minimalistic and modern.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

992

[ "4 = \\frac { 4 \\times 3 } { 1 \\times 3 } = \\frac { 1 2 } { 3 }\n" ]

The image shows a handwritten mathematical equation. The equation is written in blue ink on a white background. The equation appears to be a fraction, with the numerator being "h^4x^3" and the denominator being "h^2x^3". The equation is written in a cursive style, with the letters flowing together. The equation is centered in the image, with equal amounts of white space above and below it. The equation is the only element in the image, with no other objects or text present.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

993

[ "f ( - 1 ) \\cdot f ( 1 ) \\leq 0\n" ]

The image shows a handwritten equation in pink ink on a white background. The equation appears to be a fraction with the numerator being a single letter "f" and the denominator being a combination of the letters "f" and "k". The handwriting is slightly messy, with the lines of the equation not being perfectly straight. The overall appearance of the image is simple and minimalistic.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

994

[ "\\frac { 1 } { x + y } = \\frac { 1 } { 2 }\n" ]

The image shows a handwritten equation on a white surface. The equation is written in black ink and appears to be a mathematical expression involving the variable "y". The handwriting is somewhat messy, with some of the letters and numbers overlapping or not fully formed. The equation itself is not fully visible, as only the right side of it is shown in the image.

HME100k

difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

997

[ "x > - \\frac { 5 } { 2 }\n" ]

The image shows a handwritten mathematical expression on a white piece of paper. The expression consists of two symbols: a greater than or equal to sign (≥) and a less than or equal to sign (≤). The symbols are written in black ink and appear to be drawn with a pen or marker. The paper has a smooth texture and is free of any other markings or text. The overall appearance of the image is simple and focused on the mathematical symbols.

HME100k

very_difficult

Please write out the expression of the formula in the image using LaTeX format.

Handwritten Mathematical Expression Recognition

998

[ "\\angle B A C = \\frac { 1 } { 2 } \\angle B O C\n" ]

The image shows a handwritten mathematical equation on a white surface. The equation is written in black ink and appears to be a ratio or fraction, with the numerator being "1" and the denominator being a complex expression involving the square root of "L^2". The handwriting is somewhat messy and the equation is not fully legible due to the angle and quality of the image.