
'''simple docstring'''







from __future__ import annotations

from math import pi, pow

def 				_snake_case (		lowercase						)       ->       float:
				if side_length < 0:
								raise ValueError("""vol_cube() only accepts non-negative values"""						)
				return pow(lowercase			,    3						)

def 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				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(lowercase			,    2						) * (3 * radius - height)

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       float:
				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(lowercase			,    lowercase						)						)

				__a       :     List[str]								=	(
				    (radius_a - radius_a + centers_distance)
				    * (radius_a + radius_a - centers_distance)
				    / (2 * centers_distance)
				)
				__a       :     Tuple								=	(
				    (radius_a - radius_a + centers_distance)
				    * (radius_a + radius_a - centers_distance)
				    / (2 * centers_distance)
				)

				return vol_spherical_cap(lowercase			,    lowercase						) + vol_spherical_cap(lowercase			,    lowercase						)

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       float:

				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(lowercase			,    lowercase						)						)

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

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       float:
				if width < 0 or height < 0 or length < 0:
								raise ValueError("""vol_cuboid() only accepts non-negative values"""						)
				return float(width * height * length						)

def 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				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 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				if height < 0 or radius < 0:
								raise ValueError("""vol_right_circ_cone() only accepts non-negative values"""						)
				return pi * pow(lowercase			,    2						) * height / 3.0

def 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				if height < 0 or area_of_base < 0:
								raise ValueError("""vol_prism() only accepts non-negative values"""						)
				return float(area_of_base * height						)

def 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				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 				_snake_case (		lowercase						)       ->       float:
				if radius < 0:
								raise ValueError("""vol_sphere() only accepts non-negative values"""						)
				# Volume is 4/3 * pi * radius cubed
				return 4 / 3 * pi * pow(lowercase			,    3						)

def 				_snake_case (		lowercase						)       ->       float:
				if radius < 0:
								raise ValueError("""vol_hemisphere() only accepts non-negative values"""						)
				# Volume is radius cubed * pi * 2/3
				return pow(lowercase			,    3						) * pi * 2 / 3

def 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				if height < 0 or radius < 0:
								raise ValueError("""vol_circular_cylinder() only accepts non-negative values"""						)
				# Volume is radius squared * height * pi
				return pow(lowercase			,    2						) * height * pi

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       float:
				# Volume - (outer_radius squared - inner_radius squared) * pi * height
				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(lowercase			,    2						) - pow(lowercase			,    2						)) * height

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       float:
				# Volume is 1/3 * pi * height *
				#           (radius_1 squared + radius_2 squared + radius_1 * radius_2)
				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(lowercase			,    2						) + pow(lowercase			,    2						) + radius_a * radius_a)
				)

def 				_snake_case (		lowercase			,    lowercase						)       ->       float:
				if torus_radius < 0 or tube_radius < 0:
								raise ValueError("""vol_torus() only accepts non-negative values"""						)
				return 2 * pow(lowercase			,    2						) * torus_radius * pow(lowercase			,    2						)

def 				_snake_case (		)       ->       List[Any]:
				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()

'''simple docstring'''







def 				_snake_case (		lowercase						)       ->       int:
				if not isinstance(lowercase			,    lowercase						):
								__a       :     Union[str, Any]								=	F"""Input value of [number={number}] must be an integer"""
								raise TypeError(lowercase						)
				if number < 1:
								raise ValueError("""Input must be a positive integer"""						)
				return number * (2 * number - 1)


if __name__ == "__main__":
					import doctest

					doctest.testmod()