


from __future__ import annotations

from math import pi, pow






def 		a__       (							A__							):


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






def 		a__       (							A__,	A__							):


			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(SCREAMING_SNAKE_CASE__,	2							) * (3 * radius - height)






def 		a__       (							A__,	A__,	A__							):


			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(SCREAMING_SNAKE_CASE__,	SCREAMING_SNAKE_CASE__							)							)

			SCREAMING_SNAKE_CASE_						:			Dict       						= (
			    (radius_a - radius_a + centers_distance)
			    * (radius_a + radius_a - centers_distance)
			    / (2 * centers_distance)
			)
			SCREAMING_SNAKE_CASE_						:			str       						= (
			    (radius_a - radius_a + centers_distance)
			    * (radius_a + radius_a - centers_distance)
			    / (2 * centers_distance)
			)

			return vol_spherical_cap(SCREAMING_SNAKE_CASE__,	SCREAMING_SNAKE_CASE__							) + vol_spherical_cap(SCREAMING_SNAKE_CASE__,	SCREAMING_SNAKE_CASE__							)






def 		a__       (							A__,	A__,	A__							):


			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(SCREAMING_SNAKE_CASE__,	SCREAMING_SNAKE_CASE__							)							)

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






def 		a__       (							A__,	A__,	A__							):


			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__       (							A__,	A__							):


			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__       (							A__,	A__							):


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






def 		a__       (							A__,	A__							):


			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__       (							A__,	A__							):


			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__       (							A__							):


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






def 		a__       (							A__							):


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






def 		a__       (							A__,	A__							):


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






def 		a__       (							A__,	A__,	A__							):


			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(SCREAMING_SNAKE_CASE__,	2							) - pow(SCREAMING_SNAKE_CASE__,	2							)) * height






def 		a__       (							A__,	A__,	A__							):


			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(SCREAMING_SNAKE_CASE__,	2							) + pow(SCREAMING_SNAKE_CASE__,	2							) + radius_a * radius_a)
			)






def 		a__       (							A__,	A__							):


			if torus_radius < 0 or tube_radius < 0:
						raise ValueError('vol_torus() only accepts non-negative values'							)
			return 2 * pow(SCREAMING_SNAKE_CASE__,	2							) * torus_radius * pow(SCREAMING_SNAKE_CASE__,	2							)






def 		a__       (							):
			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

from collections.abc import Callable




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__ = 100      ,    )   ->				float:


		'''simple docstring'''


		snake_case   :    int			       =		x_start
		snake_case   :    Tuple			       =		fnc(SCREAMING_SNAKE_CASE__       )
		snake_case   :    Dict			       =		0.0

		for _ in range(SCREAMING_SNAKE_CASE__       ):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				snake_case   :    str			       =		(x_end - x_start) / steps + xa
				snake_case   :    str			       =		fnc(SCREAMING_SNAKE_CASE__       )
				area += abs(fxa + fxa       ) * (xa - xa) / 2

				# Increment step
				snake_case   :    Any			       =		xa
				snake_case   :    List[str]			       =		fxa
		return area


if __name__ == "__main__":




						def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				str:


								'''simple docstring'''


								return x**3

						print("f(x) = x^3")
						print("The area between the curve, x = -10, x = 10 and the x axis is:")
						lowercase__		    =	1_0
						while i <= 1_0_0_0_0_0:
												lowercase__		    =	trapezoidal_area(f, -5, 5, i)
												print(f"with {i} steps: {area}")
												i *= 1_0


