


"""simple docstring"""
from __future__ import annotations

from math import pi, pow






def 						lowercase				(	_snake_case		: int | float	)	->float:
	"""simple docstring"""





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






def 						lowercase				(	_snake_case		: float	,  _snake_case		: float	)	->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(_snake_case	,  2	) * (3 * radius - height)






def 						lowercase				(	_snake_case		: float	,  _snake_case		: float	,  _snake_case		: float	)	->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(_snake_case	,  _snake_case	)	)

	__snake_case      :		Optional[int]         =							(
	    (radius_a - radius_a + centers_distance)
	    * (radius_a + radius_a - centers_distance)
	    / (2 * centers_distance)
	)
	__snake_case      :		str         =							(
	    (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 						lowercase				(	_snake_case		: float	,  _snake_case		: float	,  _snake_case		: float	)	->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(_snake_case	,  _snake_case	)	)

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






def 						lowercase				(	_snake_case		: float	,  _snake_case		: float	,  _snake_case		: float	)	->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				(	_snake_case		: float	,  _snake_case		: float	)	->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				(	_snake_case		: float	,  _snake_case		: float	)	->float:
	"""simple docstring"""





	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 						lowercase				(	_snake_case		: float	,  _snake_case		: float	)	->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				(	_snake_case		: float	,  _snake_case		: float	)	->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				(	_snake_case		: float	)	->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(_snake_case	,  3	)






def 						lowercase				(	_snake_case		: float	)	->float:
	"""simple docstring"""





	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 						lowercase				(	_snake_case		: float	,  _snake_case		: float	)	->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(_snake_case	,  2	) * height * pi






def 						lowercase				(	_snake_case		: float	,  _snake_case		: float	,  _snake_case		: float	)	->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(_snake_case	,  2	) - pow(_snake_case	,  2	)) * height






def 						lowercase				(	_snake_case		: float	,  _snake_case		: float	,  _snake_case		: float	)	->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(_snake_case	,  2	) + pow(_snake_case	,  2	) + radius_a * radius_a)
	)






def 						lowercase				(	_snake_case		: float	,  _snake_case		: float	)	->float:
	"""simple docstring"""





	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 						lowercase				(	)	->Optional[Any]:
	"""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()






def   a_					(_lowerCAmelCase  :   int       )->				str:
    if not isinstance(_lowerCAmelCase			,	_lowerCAmelCase       ):
        snake_case:						Optional[Any]         =   (
            """operation can not be conducted on a object of type """
            F"{type(_lowerCAmelCase       ).__name__}"
        )
        raise TypeError(_lowerCAmelCase       )
    snake_case:						List[Any]         =   """"""
    for _ in range(0			,	32       ):
        bit_string += str(number % 2       )
        snake_case:						Any         =   number >> 1
    return bit_string

def   a_					(_lowerCAmelCase  :   int       )->				str:
    if number < 0:
        raise ValueError("""the value of input must be positive"""       )
    elif isinstance(_lowerCAmelCase			,	_lowerCAmelCase       ):
        raise TypeError("""Input value must be a 'int' type"""       )
    elif isinstance(_lowerCAmelCase			,	_lowerCAmelCase       ):
        raise TypeError("""'<' not supported between instances of 'str' and 'int'"""       )
    snake_case:						Optional[Any]         =   0
    # iterator over [1 to 32],since we are dealing with 32 bit integer
    for _ in range(1			,	33       ):
        # left shift the bits by unity
        snake_case:						Dict         =   result << 1
        # get the end bit
        snake_case:						Union[str, Any]         =   number % 2
        # right shift the bits by unity
        snake_case:						Union[str, Any]         =   number >> 1
        # add that bit to our ans
        snake_case:						Tuple         =   result | end_bit
    return get_reverse_bit_string(_lowerCAmelCase       )


if __name__ == "__main__":
    import doctest

    doctest.testmod()


