



"""simple docstring"""


from math import pi, sqrt, tan







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if side_length < 0:
								raise ValueError('''surface_area_cube() only accepts non-negative values'''				)
				return 6 * side_length**2







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if length < 0 or breadth < 0 or height < 0:
								raise ValueError('''surface_area_cuboid() only accepts non-negative values'''				)
				return 2 * ((length * breadth) + (breadth * height) + (length * height))







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius < 0:
								raise ValueError('''surface_area_sphere() only accepts non-negative values'''				)
				return 4 * pi * radius**2







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius < 0:
								raise ValueError('''surface_area_hemisphere() only accepts non-negative values'''				)
				return 3 * pi * radius**2







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius < 0 or height < 0:
								raise ValueError('''surface_area_cone() only accepts non-negative values'''				)
				return pi * radius * (radius + (height**2 + radius**2) ** 0.5)







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius_a < 0 or radius_a < 0 or height < 0:
								raise ValueError(
								    '''surface_area_conical_frustum() only accepts non-negative values'''				)
				_UpperCAmelCase					=    (height**2 + (radius_a - radius_a) ** 2) ** 0.5
				return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius < 0 or height < 0:
								raise ValueError('''surface_area_cylinder() only accepts non-negative values'''				)
				return 2 * pi * radius * (height + radius)







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if torus_radius < 0 or tube_radius < 0:
								raise ValueError('''surface_area_torus() only accepts non-negative values'''				)
				if torus_radius < tube_radius:
								raise ValueError(
								    '''surface_area_torus() does not support spindle or self intersecting tori'''				)
				return 4 * pow(_SCREAMING_SNAKE_CASE					,     2				) * torus_radius * tube_radius







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if length < 0 or width < 0:
								raise ValueError('''area_rectangle() only accepts non-negative values'''				)
				return length * width







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if side_length < 0:
								raise ValueError('''area_square() only accepts non-negative values'''				)
				return side_length**2







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if base < 0 or height < 0:
								raise ValueError('''area_triangle() only accepts non-negative values'''				)
				return (base * height) / 2







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if sidea < 0 or sidea < 0 or sidea < 0:
								raise ValueError('''area_triangle_three_sides() only accepts non-negative values'''				)
				elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
								raise ValueError('''Given three sides do not form a triangle'''				)
				_UpperCAmelCase					=    (sidea + sidea + sidea) / 2
				_UpperCAmelCase					=    sqrt(
				    semi_perimeter
				    * (semi_perimeter - sidea)
				    * (semi_perimeter - sidea)
				    * (semi_perimeter - sidea)				)
				return area







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if base < 0 or height < 0:
								raise ValueError('''area_parallelogram() only accepts non-negative values'''				)
				return base * height







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if basea < 0 or basea < 0 or height < 0:
								raise ValueError('''area_trapezium() only accepts non-negative values'''				)
				return 1 / 2 * (basea + basea) * height







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius < 0:
								raise ValueError('''area_circle() only accepts non-negative values'''				)
				return pi * radius**2







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if radius_x < 0 or radius_y < 0:
								raise ValueError('''area_ellipse() only accepts non-negative values'''				)
				return pi * radius_x * radius_y







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if diagonal_a < 0 or diagonal_a < 0:
								raise ValueError('''area_rhombus() only accepts non-negative values'''				)
				return 1 / 2 * diagonal_a * diagonal_a







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						float				):






				'''simple docstring'''



				if not isinstance(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				) or sides < 3:
								raise ValueError(
								    '''area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'''				)
				elif length < 0:
								raise ValueError(
								    '''area_reg_polygon() only accepts non-negative values as \
length of a side'''				)
				return (sides * length**2) / (4 * tan(pi / sides				))
				return (sides * length**2) / (4 * tan(pi / sides				))


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

						print("[DEMO] Areas of various geometric shapes: \n")
						print(f'''Rectangle: {area_rectangle(10, 20) = }''')
						print(f'''Square: {area_square(10) = }''')
						print(f'''Triangle: {area_triangle(10, 10) = }''')
						print(f'''Triangle: {area_triangle_three_sides(5, 12, 13) = }''')
						print(f'''Parallelogram: {area_parallelogram(10, 20) = }''')
						print(f'''Rhombus: {area_rhombus(10, 20) = }''')
						print(f'''Trapezium: {area_trapezium(10, 20, 30) = }''')
						print(f'''Circle: {area_circle(20) = }''')
						print(f'''Ellipse: {area_ellipse(10, 20) = }''')
						print("\nSurface Areas of various geometric shapes: \n")
						print(f'''Cube: {surface_area_cube(20) = }''')
						print(f'''Cuboid: {surface_area_cuboid(10, 20, 30) = }''')
						print(f'''Sphere: {surface_area_sphere(20) = }''')
						print(f'''Hemisphere: {surface_area_hemisphere(20) = }''')
						print(f'''Cone: {surface_area_cone(10, 20) = }''')
						print(f'''Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }''')
						print(f'''Cylinder: {surface_area_cylinder(10, 20) = }''')
						print(f'''Torus: {surface_area_torus(20, 10) = }''')
						print(f'''Equilateral Triangle: {area_reg_polygon(3, 10) = }''')
						print(f'''Square: {area_reg_polygon(4, 10) = }''')
						print(f'''Reqular Pentagon: {area_reg_polygon(5, 10) = }''')








"""simple docstring"""


import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


__A   :							Any										=   "\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n"


__A   :							Optional[Any]										=   "\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.\n"


__A   :							Tuple										=   r"\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")\n\nExamples:\n    >>> metric = datasets.load_metric(\"competition_math\")\n    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])\n    >>> print(results)\n    {'accuracy': 1.0}\n"
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION			,							_KWARGS_DESCRIPTION)
class 			_a (					datasets.Metric):
			"""simple docstring"""



			def  lowercase__						(		self     :    List[Any]   )->Dict:
							return datasets.MetricInfo(
							    description=_DESCRIPTION				,   citation=_CITATION				,   inputs_description=_KWARGS_DESCRIPTION				,   features=datasets.Features(
							        {
							            '''predictions''': datasets.Value('''string'''   ),
							            '''references''': datasets.Value('''string'''   ),
							        }   )				,   homepage='''https://github.com/hendrycks/math'''				,   codebase_urls=['''https://github.com/hendrycks/math''']				,   )



			def  lowercase__						(		self     :    int				,   __UpperCamelCase     :    List[str]				,   __UpperCamelCase     :    Union[str, Any]   )->Tuple:
							_UpperCAmelCase					=    0.0
							for i, j in zip(__UpperCamelCase				,   __UpperCamelCase   ):
											n_correct += 1.0 if math_equivalence.is_equiv(__UpperCamelCase				,   __UpperCamelCase   ) else 0.0
							_UpperCAmelCase					=    n_correct / len(__UpperCamelCase   )
							return {
							    "accuracy": accuracy,
							}



