
from __future__ import annotations

from math import pi, pow






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






def     lowerCamelCase__				(   a						,						a ) ->  float:
   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(_lowerCAmelCase						,						2 ) * (3 * radius - height)






def     lowerCamelCase__				(   a						,						a						,						a ) ->  float:
   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(_lowerCAmelCase						,						_lowerCAmelCase ) )

   _A:    int						     =			(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )
   _A:    List[str]						     =			(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )

   return vol_spherical_cap(_lowerCAmelCase						,						_lowerCAmelCase ) + vol_spherical_cap(_lowerCAmelCase						,						_lowerCAmelCase )






def     lowerCamelCase__				(   a						,						a						,						a ) ->  float:

   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(_lowerCAmelCase						,						_lowerCAmelCase ) )

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






def     lowerCamelCase__				(   a						,						a						,						a ) ->  float:
   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__				(   a						,						a ) ->  float:
   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__				(   a						,						a ) ->  float:
   if height < 0 or radius < 0:
      raise ValueError('''vol_right_circ_cone() only accepts non-negative values''' )
   return pi * pow(_lowerCAmelCase						,						2 ) * height / 3.0






def     lowerCamelCase__				(   a						,						a ) ->  float:
   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__				(   a						,						a ) ->  float:
   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__				(   a ) ->  float:
   if radius < 0:
      raise ValueError('''vol_sphere() only accepts non-negative values''' )
   # Volume is 4/3 * pi * radius cubed
   return 4 / 3 * pi * pow(_lowerCAmelCase						,						3 )






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






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






def     lowerCamelCase__				(   a						,						a						,						a ) ->  float:
   # 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(_lowerCAmelCase						,						2 ) - pow(_lowerCAmelCase						,						2 )) * height






def     lowerCamelCase__				(   a						,						a						,						a ) ->  float:
   # 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(_lowerCAmelCase						,						2 ) + pow(_lowerCAmelCase						,						2 ) + radius_a * radius_a)
   )






def     lowerCamelCase__				(   a						,						a ) ->  float:
   if torus_radius < 0 or tube_radius < 0:
      raise ValueError('''vol_torus() only accepts non-negative values''' )
   return 2 * pow(_lowerCAmelCase						,						2 ) * torus_radius * pow(_lowerCAmelCase						,						2 )






def     lowerCamelCase__				(   ) ->  Any:
   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()


