code: 
  
  
  from __future__ import annotations
  
  from math import pi, pow
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase     )    ->float:
  
  
  
  
  
  
  
        """simple docstring"""
  
        if side_length < 0:
              raise ValueError('''vol_cube() only accepts non-negative values'''     )
        return pow(_UpperCamelCase,    3     )
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->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(_UpperCamelCase,    2     ) * (3 * radius - height)
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase     )    ->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(_UpperCamelCase,    _UpperCamelCase     )     )
  
        lowercase			:   List[str]					   =		(
            (radius_a - radius_a + centers_distance)
            * (radius_a + radius_a - centers_distance)
            / (2 * centers_distance)
        )
        lowercase			:   Any					   =		(
            (radius_a - radius_a + centers_distance)
            * (radius_a + radius_a - centers_distance)
            / (2 * centers_distance)
        )
  
        return vol_spherical_cap(_UpperCamelCase,    _UpperCamelCase     ) + vol_spherical_cap(_UpperCamelCase,    _UpperCamelCase     )
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase     )    ->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(_UpperCamelCase,    _UpperCamelCase     )     )
  
        return (
            vol_sphere(_UpperCamelCase     )
            + vol_sphere(_UpperCamelCase     )
            - vol_spheres_intersect(_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase     )
        )
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase     )    ->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	(						_UpperCamelCase,    _UpperCamelCase     )    ->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	(						_UpperCamelCase,    _UpperCamelCase     )    ->float:
  
  
  
  
  
  
  
        """simple docstring"""
  
        if height < 0 or radius < 0:
              raise ValueError('''vol_right_circ_cone() only accepts non-negative values'''     )
        return pi * pow(_UpperCamelCase,    2     ) * height / 3.0
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->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	(						_UpperCamelCase,    _UpperCamelCase     )    ->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	(						_UpperCamelCase     )    ->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(_UpperCamelCase,    3     )
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase     )    ->float:
  
  
  
  
  
  
  
        """simple docstring"""
  
        if radius < 0:
              raise ValueError('''vol_hemisphere() only accepts non-negative values'''     )
        # Volume is radius cubed * pi * 2/3
        return pow(_UpperCamelCase,    3     ) * pi * 2 / 3
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->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(_UpperCamelCase,    2     ) * height * pi
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase     )    ->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(_UpperCamelCase,    2     ) - pow(_UpperCamelCase,    2     )) * height
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase,    _UpperCamelCase     )    ->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(_UpperCamelCase,    2     ) + pow(_UpperCamelCase,    2     ) + radius_a * radius_a)
        )
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->float:
  
  
  
  
  
  
  
        """simple docstring"""
  
        if torus_radius < 0 or tube_radius < 0:
              raise ValueError('''vol_torus() only accepts non-negative values'''     )
        return 2 * pow(_UpperCamelCase,    2     ) * torus_radius * pow(_UpperCamelCase,    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()
  
  
style_context: 
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available
  
  
  __a   				=      {
      '''configuration_decision_transformer''': [
          '''DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
          '''DecisionTransformerConfig''',
      ],
  }
  
  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    __a   				=      [
        '''DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''DecisionTransformerGPT2Model''',
        '''DecisionTransformerGPT2PreTrainedModel''',
        '''DecisionTransformerModel''',
        '''DecisionTransformerPreTrainedModel''',
    ]
  
  
  if TYPE_CHECKING:
    from .configuration_decision_transformer import (
        DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
        DecisionTransformerConfig,
    )
  
    try:
      if not is_torch_available():
        raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
      pass
    else:
      from .modeling_decision_transformer import (
          DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          DecisionTransformerGPTaModel,
          DecisionTransformerGPTaPreTrainedModel,
          DecisionTransformerModel,
          DecisionTransformerPreTrainedModel,
      )
  
  
  else:
    import sys
  
    __a   				=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
  
  