



"""simple docstring"""


from __future__ import annotations

from math import pi, pow

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

def 				_lowerCAmelCase   (     lowercase_	,			lowercase_		):
						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 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_		):
						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_		)		)

						UpperCAmelCase    =				(
						    (radius_a - radius_a + centers_distance)
						    * (radius_a + radius_a - centers_distance)
						    / (2 * centers_distance)
						)
						UpperCAmelCase    =				(
						    (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 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_		):

						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 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_		):
						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   (     lowercase_	,			lowercase_		):
						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   (     lowercase_	,			lowercase_		):
						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 				_lowerCAmelCase   (     lowercase_	,			lowercase_		):
						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   (     lowercase_	,			lowercase_		):
						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   (     lowercase_		):
						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 				_lowerCAmelCase   (     lowercase_		):
						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 				_lowerCAmelCase   (     lowercase_	,			lowercase_		):
						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 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_		):
						# 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(lowercase_	,			2		) - pow(lowercase_	,			2		)) * height

def 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_		):
						# 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(lowercase_	,			2		) + pow(lowercase_	,			2		) + radius_a * radius_a)
						)

def 				_lowerCAmelCase   (     lowercase_	,			lowercase_		):
						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 				_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"""


from math import exp

def 				_lowerCAmelCase   (     lowercase_		):
						return 8 * x - 2 * exp(-x		)

def 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_		):
						UpperCAmelCase    =				lower_bound
						UpperCAmelCase    =				upper_bound
						for _ in range(0	,			lowercase_		):
												UpperCAmelCase   ,					UpperCAmelCase    =				xa, xa - (f(lowercase_		) * (xa - xa)) / (f(lowercase_		) - f(lowercase_		))
						return xa


if __name__ == "__main__":
				print(f'''Example: {secant_method(1, 3, 2)}''')





