
'''simple docstring'''


from __future__ import annotations

from math import pi, pow




def lowercase_		(				_lowercase			)       ->							float:
					'''simple docstring'''

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




def lowercase_		(				_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 lowercase_		(				_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			)			)

					lowerCamelCase_   : List[str]       =						(
					    (radius_a - radius_a + centers_distance)
					    * (radius_a + radius_a - centers_distance)
					    / (2 * centers_distance)
					)
					lowerCamelCase_   : Dict       =						(
					    (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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				_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 lowercase_		(				)       ->							List[str]:
					'''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'''


def lowercase_		(				_lowercase			)       ->							int:
					'''simple docstring'''

					if not isinstance(_lowercase     ,    _lowercase			):
										raise TypeError('''recursive_lucas_number accepts only integer arguments.'''			)
					if n_th_number == 0:
										return 2
					if n_th_number == 1:
										return 1

					return recursive_lucas_number(n_th_number - 1			) + recursive_lucas_number(
					    n_th_number - 2			)




def lowercase_		(				_lowercase			)       ->							int:
					'''simple docstring'''

					if not isinstance(_lowercase     ,    _lowercase			):
										raise TypeError('''dynamic_lucas_number accepts only integer arguments.'''			)
					lowerCamelCase_, lowerCamelCase_   : List[Any]       =						2, 1
					for _ in range(_lowercase			):
										lowerCamelCase_, lowerCamelCase_   : Dict       =						b, a + b
					return a


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					__lowercase							:				Any					=       int(input('''Enter the number of terms in lucas series:\n''').strip())
					print('''Using recursive function to calculate lucas series:''')
					print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
					print('''\nUsing dynamic function to calculate lucas series:''')
					print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))


