"""simple docstring"""







from __future__ import annotations

from math import pi, pow


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


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     2     ) * (3 * radius - height)


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     UpperCAmelCase__     )     )

						UpperCAmelCase__   		=						(
						    (radius_a - radius_a + centers_distance)
						    * (radius_a + radius_a - centers_distance)
						    / (2 * centers_distance)
						)
						UpperCAmelCase__   		=						(
						    (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 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     UpperCAmelCase__     )     )

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


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		float:
						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 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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 					a__ (						UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     3     )


def 					a__ (						UpperCAmelCase__    :     float     )->		float:
						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 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     2     ) * height * pi


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     2     ) - pow(UpperCAmelCase__						,     2     )) * height


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		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(UpperCAmelCase__						,     2     ) + pow(UpperCAmelCase__						,     2     ) + radius_a * radius_a)
						)


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     float     )->		float:
						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 					a__ (						)->		Optional[int]:
						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"""







import safs


class      _lowercase						(				safs.SaFileSystem					):
				pass

