





"""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_		)		)

    __A					:		Optional[int]						=  (
        (radius_a - radius_a + centers_distance)
        * (radius_a + radius_a - centers_distance)
        / (2 * centers_distance)
    )
    __A					:		Union[str, Any]						=  (
        (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  (     )     ->Tuple:



    '''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  (     snake_case_						:						list		)     ->list:



    '''simple docstring'''







    for insert_index, insert_value in enumerate(collection[1:]		):
        __A					:		Any						=  insert_index
        while insert_index >= 0 and insert_value < collection[insert_index]:
            __A					:		List[Any]						=  collection[insert_index]
            insert_index -= 1
        if insert_index != temp_index:
            __A					:		str						=  insert_value
    return collection


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

       testmod()

       a_				=    input("""Enter numbers separated by a comma:\n""").strip()
       a_				=    [int(item) for item in user_input.split(""",""")]
       print(f'''{insertion_sort(unsorted) = }''')




