




'''simple docstring'''







import math






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if not isinstance(lowercase_						,							lowercase_  ):
				_snake_case	       =       f'''Input value of [number={number}] must be an integer'''
				raise TypeError(lowercase_  )
		if number < 1:
				_snake_case	       =       f'''Input value of [number={number}] must be a positive integer'''
				raise ValueError(lowercase_  )
		_snake_case	       =       [number]
		while number != 1:
				if number % 2 == 0:
						_snake_case	       =       math.floor(math.sqrt(lowercase_  )  )
				else:
						_snake_case	       =       math.floor(
						    math.sqrt(lowercase_  ) * math.sqrt(lowercase_  ) * math.sqrt(lowercase_  )  )
				sequence.append(lowercase_  )
		return sequence


if __name__ == "__main__":
						import doctest

						doctest.testmod()











'''simple docstring'''







from __future__ import annotations

from math import pi, pow






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







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






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''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(lowercase_						,							2  ) * (3 * radius - height)






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''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(lowercase_						,							lowercase_  )  )

		_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(lowercase_						,							lowercase_  ) + vol_spherical_cap(lowercase_						,							lowercase_  )






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''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(lowercase_						,							lowercase_  )  )

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






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''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 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''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 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		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 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''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 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''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 		_lowercase		(	lowercase_  ):



		'''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(lowercase_						,							3  )






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		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 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''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(lowercase_						,							2  ) * height * pi






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''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(lowercase_						,							2  ) - pow(lowercase_						,							2  )) * height






def 		_lowercase		(	lowercase_						,							lowercase_						,							lowercase_  ):



		'''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(lowercase_						,							2  ) + pow(lowercase_						,							2  ) + radius_a * radius_a)
		)






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		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 		_lowercase		(	):



		'''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()





