






'''simple docstring'''





from __future__ import annotations

from math import pi, pow



def 			__UpperCAmelCase				(lowercase__				)		->				float:

						'''simple docstring'''


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



def 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				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(lowercase__	,2				) * (3 * radius - height)



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__				)		->				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(lowercase__	,lowercase__				)				)

						a_				     =   (
						    (radius_a - radius_a + centers_distance)
						    * (radius_a + radius_a - centers_distance)
						    / (2 * centers_distance)
						)
						a_				     =   (
						    (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 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__				)		->				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(lowercase__	,lowercase__				)				)

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



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__				)		->				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				(lowercase__	,lowercase__				)		->				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				(lowercase__	,lowercase__				)		->				float:

						'''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 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				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				(lowercase__	,lowercase__				)		->				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				(lowercase__				)		->				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(lowercase__	,3				)



def 			__UpperCAmelCase				(lowercase__				)		->				float:

						'''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 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				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(lowercase__	,2				) * height * pi



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__				)		->				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(lowercase__	,2				) - pow(lowercase__	,2				)) * height



def 			__UpperCAmelCase				(lowercase__	,lowercase__	,lowercase__				)		->				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(lowercase__	,2				) + pow(lowercase__	,2				) + radius_a * radius_a)
						)



def 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				float:

						'''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 			__UpperCAmelCase				()		->				Tuple:

						'''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()











'''simple docstring'''





from __future__ import annotations





class 		SCREAMING_SNAKE_CASE__   :



		def __init__(    self:    List[str]				,   a:    int = 0)  ->None:






								'''simple docstring'''


								a_				     =   value
								a_				     =   None
								a_				     =   None





def 			__UpperCAmelCase				(lowercase__	,lowercase__				)		->				Node | None:

						'''simple docstring'''


						if treea is None:
												return treea
						if treea is None:
												return treea

						a_				     =   treea.value + treea.value
						a_				     =   merge_two_binary_trees(treea.left	,treea.left				)
						a_				     =   merge_two_binary_trees(treea.right	,treea.right				)
						return treea



def 			__UpperCAmelCase				(lowercase__				)		->				None:

						'''simple docstring'''


						if root:
												print(root.value				)
												print_preorder(root.left				)
												print_preorder(root.right				)


if __name__ == "__main__":
							a_      = Node(1)
							a_      = Node(2)
							a_      = Node(3)
							a_      = Node(4)

							a_      = Node(2)
							a_      = Node(4)
							a_      = Node(6)
							a_      = Node(9)
							a_      = Node(5)

							print('Tree1 is: ')
							print_preorder(treea)
							print('Tree2 is: ')
							print_preorder(treea)
							a_      = merge_two_binary_trees(treea, treea)
							print('Merged Tree is: ')
							print_preorder(merged_tree)



