




'''simple docstring'''






from __future__ import annotations

from math import pi, pow

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

def       __lowerCAmelCase (   snake_case__ ,				snake_case__						):
			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(snake_case__ ,				2						) * (3 * radius - height)

def       __lowerCAmelCase (   snake_case__ ,				snake_case__ ,				snake_case__						):
			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(snake_case__ ,				snake_case__						)						)

			__UpperCamelCase				:      Optional[Any]									=       (
			    (radius_a - radius_a + centers_distance)
			    * (radius_a + radius_a - centers_distance)
			    / (2 * centers_distance)
			)
			__UpperCamelCase				:      Optional[Any]									=       (
			    (radius_a - radius_a + centers_distance)
			    * (radius_a + radius_a - centers_distance)
			    / (2 * centers_distance)
			)

			return vol_spherical_cap(snake_case__ ,				snake_case__						) + vol_spherical_cap(snake_case__ ,				snake_case__						)

def       __lowerCAmelCase (   snake_case__ ,				snake_case__ ,				snake_case__						):

			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(snake_case__ ,				snake_case__						)						)

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

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

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

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

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

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

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

def       __lowerCAmelCase (   snake_case__ ,				snake_case__ ,				snake_case__						):
			# 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(snake_case__ ,				2						) - pow(snake_case__ ,				2						)) * height

def       __lowerCAmelCase (   snake_case__ ,				snake_case__ ,				snake_case__						):
			# 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(snake_case__ ,				2						) + pow(snake_case__ ,				2						) + radius_a * radius_a)
			)

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

def       __lowerCAmelCase (   ):
			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       __lowerCAmelCase (   snake_case__ = 4_000_000						):
			__UpperCamelCase				:      Tuple									=       1
			__UpperCamelCase				:      int									=       2
			__UpperCamelCase				:      str									=       0
			while j <= n:
						if j % 2 == 0:
									total += j
						__UpperCamelCase		, __UpperCamelCase				:      List[Any]									=       j, i + j

			return total


if __name__ == "__main__":
				print(f'{solution() = }')



