


from __future__ import annotations

from math import pi, pow







def 							UpperCAmelCase				(     UpperCAmelCase      )->		float:







					'''simple docstring'''



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







def 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		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      )      )

					SCREAMING_SNAKE_CASE_	      =       (
					    (radius_a - radius_a + centers_distance)
					    * (radius_a + radius_a - centers_distance)
					    / (2 * centers_distance)
					)
					SCREAMING_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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		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 							UpperCAmelCase				(     )->		Optional[Any]:







					'''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()






from __future__ import annotations

class 						snake_case			:
			'''simple docstring'''

			def __init__(	self     :     int							,							lowerCAmelCase_     :     int					)					->					None:




								"""simple docstring"""






								SCREAMING_SNAKE_CASE_	      =       value
								SCREAMING_SNAKE_CASE_	      =       None
								SCREAMING_SNAKE_CASE_	      =       None

class 						snake_case			:
			'''simple docstring'''

			UpperCAmelCase       :       int

			def __init__(	self     :     Union[str, Any]					)					->					None:




								"""simple docstring"""






								SCREAMING_SNAKE_CASE_	      =       0

			def _lowercase (	self     :     Optional[int]							,							lowerCAmelCase_     :     Node | None							,							lowerCAmelCase_     :     int					)					->					None:




								"""simple docstring"""






								if node is None:
													return

								if path_sum == self.target:
													self.paths += 1

								if node.left:
													self.depth_first_search(node.left							,							path_sum + node.left.value					)
								if node.right:
													self.depth_first_search(node.right							,							path_sum + node.right.value					)




			def _lowercase (	self     :     str							,							lowerCAmelCase_     :     Node | None							,							lowerCAmelCase_     :     int | None = None					)					->					int:




								"""simple docstring"""






								if node is None:
													return 0
								if target is not None:
													SCREAMING_SNAKE_CASE_	      =       target

								self.depth_first_search(lowerCAmelCase_							,							node.value					)
								self.path_sum(node.left					)
								self.path_sum(node.right					)

								return self.paths


if __name__ == "__main__":
		import doctest

		doctest.testmod()


