





from __future__ import annotations

from math import pi, pow





def     lowerCamelCase__  (  UpperCamelCase__      :							int | float    )      ->			float:



					'''simple docstring'''




					if side_length < 0:
										raise ValueError('vol_cube() only accepts non-negative values'    )
					return pow(UpperCamelCase__							,     3    )





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if height < 0 or radius < 0:
										raise ValueError('vol_spherical_cap() only accepts non-negative values'    )
					# Volume is 1/3 pi * height squared * (3 * radius - height)
					return 1 / 3 * pi * pow(UpperCamelCase__							,     2    ) * (3 * radius - height)





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if radius_a < 0 or radius_a < 0 or centers_distance < 0:
										raise ValueError('vol_spheres_intersect() only accepts non-negative values'    )
					if centers_distance == 0:
										return vol_sphere(min(UpperCamelCase__							,     UpperCamelCase__    )    )

					_snake_case						=					(
					    (radius_a - radius_a + centers_distance)
					    * (radius_a + radius_a - centers_distance)
					    / (2 * centers_distance)
					)
					_snake_case						=					(
					    (radius_a - radius_a + centers_distance)
					    * (radius_a + radius_a - centers_distance)
					    / (2 * centers_distance)
					)

					return vol_spherical_cap(UpperCamelCase__							,     UpperCamelCase__    ) + vol_spherical_cap(UpperCamelCase__							,     UpperCamelCase__    )





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
										raise ValueError(
										    'vol_spheres_union() only accepts non-negative values, non-zero radius'    )

					if centers_distance == 0:
										return vol_sphere(max(UpperCamelCase__							,     UpperCamelCase__    )    )

					return (
					    vol_sphere(UpperCamelCase__    )
					    + vol_sphere(UpperCamelCase__    )
					    - vol_spheres_intersect(UpperCamelCase__							,     UpperCamelCase__							,     UpperCamelCase__    )
					)





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




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





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if height < 0 or area_of_base < 0:
										raise ValueError('vol_cone() only accepts non-negative values'    )
					return area_of_base * height / 3.0





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if height < 0 or radius < 0:
										raise ValueError('vol_right_circ_cone() only accepts non-negative values'    )
					return pi * pow(UpperCamelCase__							,     2    ) * height / 3.0





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if height < 0 or area_of_base < 0:
										raise ValueError('vol_prism() only accepts non-negative values'    )
					return float(area_of_base * height    )





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if height < 0 or area_of_base < 0:
										raise ValueError('vol_pyramid() only accepts non-negative values'    )
					return area_of_base * height / 3.0





def     lowerCamelCase__  (  UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if radius < 0:
										raise ValueError('vol_sphere() only accepts non-negative values'    )
					# Volume is 4/3 * pi * radius cubed
					return 4 / 3 * pi * pow(UpperCamelCase__							,     3    )





def     lowerCamelCase__  (  UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if radius < 0:
										raise ValueError('vol_hemisphere() only accepts non-negative values'    )
					# Volume is radius cubed * pi * 2/3
					return pow(UpperCamelCase__							,     3    ) * pi * 2 / 3





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if height < 0 or radius < 0:
										raise ValueError('vol_circular_cylinder() only accepts non-negative values'    )
					# Volume is radius squared * height * pi
					return pow(UpperCamelCase__							,     2    ) * height * pi





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if inner_radius < 0 or outer_radius < 0 or height < 0:
										raise ValueError(
										    'vol_hollow_circular_cylinder() only accepts non-negative values'    )
					if outer_radius <= inner_radius:
										raise ValueError('outer_radius must be greater than inner_radius'    )
					return pi * (pow(UpperCamelCase__							,     2    ) - pow(UpperCamelCase__							,     2    )) * height





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if radius_a < 0 or radius_a < 0 or height < 0:
										raise ValueError('vol_conical_frustum() only accepts non-negative values'    )
					return (
					    1
					    / 3
					    * pi
					    * height
					    * (pow(UpperCamelCase__							,     2    ) + pow(UpperCamelCase__							,     2    ) + radius_a * radius_a)
					)





def     lowerCamelCase__  (  UpperCamelCase__      :							float							,     UpperCamelCase__      :							float    )      ->			float:



					'''simple docstring'''




					if torus_radius < 0 or tube_radius < 0:
										raise ValueError('vol_torus() only accepts non-negative values'    )
					return 2 * pow(UpperCamelCase__							,     2    ) * torus_radius * pow(UpperCamelCase__							,     2    )





def     lowerCamelCase__  (  )      ->			str:



					'''simple docstring'''




					print('Volumes:'    )
					print(F'''Cube: {vol_cube(2    ) = }'''    )  # = 8
					print(F'''Cuboid: {vol_cuboid(2							,     2							,     2    ) = }'''    )  # = 8
					print(F'''Cone: {vol_cone(2							,     2    ) = }'''    )  # ~= 1.33
					print(F'''Right Circular Cone: {vol_right_circ_cone(2							,     2    ) = }'''    )  # ~= 8.38
					print(F'''Prism: {vol_prism(2							,     2    ) = }'''    )  # = 4
					print(F'''Pyramid: {vol_pyramid(2							,     2    ) = }'''    )  # ~= 1.33
					print(F'''Sphere: {vol_sphere(2    ) = }'''    )  # ~= 33.5
					print(F'''Hemisphere: {vol_hemisphere(2    ) = }'''    )  # ~= 16.75
					print(F'''Circular Cylinder: {vol_circular_cylinder(2							,     2    ) = }'''    )  # ~= 25.1
					print(F'''Torus: {vol_torus(2							,     2    ) = }'''    )  # ~= 157.9
					print(F'''Conical Frustum: {vol_conical_frustum(2							,     2							,     4    ) = }'''    )  # ~= 58.6
					print(F'''Spherical cap: {vol_spherical_cap(1							,     2    ) = }'''    )  # ~= 5.24
					print(F'''Spheres intersetion: {vol_spheres_intersect(2							,     2							,     1    ) = }'''    )  # ~= 21.21
					print(F'''Spheres union: {vol_spheres_union(2							,     2							,     1    ) = }'''    )  # ~= 45.81
					print(
					    F'''Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1							,     2							,     3    ) = }'''    )  # ~= 28.3


if __name__ == "__main__":
					main()










import math
from timeit import timeit





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			int:



					'''simple docstring'''




					_snake_case						=					0
					_snake_case						=					abs(UpperCamelCase__    )
					while True:
										_snake_case						=					n // 10
										digits += 1
										if n == 0:
															break
					return digits





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			int:



					'''simple docstring'''




					return 1 if n == 0 else math.floor(math.log(abs(UpperCamelCase__    )							,     10    ) + 1    )





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			int:



					'''simple docstring'''




					return len(str(abs(UpperCamelCase__    )    )    )





def     lowerCamelCase__  (  )      ->			None:



					'''simple docstring'''




					from collections.abc import Callable

					def benchmark_a_function(UpperCamelCase__      :							Callable							,     UpperCamelCase__      :							int    ) -> None:
										_snake_case						=					F'''{func.__name__}({value})'''
										_snake_case						=					timeit(F'''__main__.{call}'''							,     setup='import __main__'    )
										print(F'''{call}: {func(UpperCamelCase__    )} -- {timing} seconds'''    )

					for value in (262_144, 1_125_899_906_842_624, 1_267_650_600_228_229_401_496_703_205_376):
										for func in (num_digits, num_digits_fast, num_digits_faster):
															benchmark_a_function(UpperCamelCase__							,     UpperCamelCase__    )
										print()


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					benchmark()



