"""simple docstring"""







from __future__ import annotations

from math import pi, pow



def       A__    (	lowercase_     :	int | float						)  ->							float:
   if side_length < 0:
      raise ValueError('vol_cube() only accepts non-negative values'						)
   return pow(lowercase_      , 3						)



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , 2						) * (3 * radius - height)



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , lowercase_						)						)

   __lowerCamelCase    		=					(
       (radius_a - radius_a + centers_distance)
       * (radius_a + radius_a - centers_distance)
       / (2 * centers_distance)
   )
   __lowerCamelCase    		=					(
       (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       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , lowercase_						)						)

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



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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       A__    (	lowercase_     :	float						)  ->							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(lowercase_      , 3						)



def       A__    (	lowercase_     :	float						)  ->							float:
   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       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , 2						) * height * pi



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , 2						) - pow(lowercase_      , 2						)) * height



def       A__    (	lowercase_     :	float      , lowercase_     :	float      , lowercase_     :	float						)  ->							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(lowercase_      , 2						) + pow(lowercase_      , 2						) + radius_a * radius_a)
   )



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   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       A__    (	)  ->							Optional[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()











'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


_UpperCamelCase									=      {'''configuration_t5''': ['''T5_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''T5Config''', '''T5OnnxConfig''']}

try:
					if not is_sentencepiece_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					_UpperCamelCase									=      ['''T5Tokenizer''']

try:
					if not is_tokenizers_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					_UpperCamelCase									=      ['''T5TokenizerFast''']

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					_UpperCamelCase									=      [
					    '''T5_PRETRAINED_MODEL_ARCHIVE_LIST''',
					    '''T5EncoderModel''',
					    '''T5ForConditionalGeneration''',
					    '''T5Model''',
					    '''T5PreTrainedModel''',
					    '''load_tf_weights_in_t5''',
					    '''T5ForQuestionAnswering''',
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					_UpperCamelCase									=      [
					    '''TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST''',
					    '''TFT5EncoderModel''',
					    '''TFT5ForConditionalGeneration''',
					    '''TFT5Model''',
					    '''TFT5PreTrainedModel''',
					]

try:
					if not is_flax_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					_UpperCamelCase									=      [
					    '''FlaxT5EncoderModel''',
					    '''FlaxT5ForConditionalGeneration''',
					    '''FlaxT5Model''',
					    '''FlaxT5PreTrainedModel''',
					]


if TYPE_CHECKING:
					from .configuration_ta import T5_PRETRAINED_CONFIG_ARCHIVE_MAP, TaConfig, TaOnnxConfig

					try:
										if not is_sentencepiece_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_ta import TaTokenizer

					try:
										if not is_tokenizers_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_ta_fast import TaTokenizerFast

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_ta import (
										    T5_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TaEncoderModel,
										    TaForConditionalGeneration,
										    TaForQuestionAnswering,
										    TaModel,
										    TaPreTrainedModel,
										    load_tf_weights_in_ta,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_ta import (
										    TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TFTaEncoderModel,
										    TFTaForConditionalGeneration,
										    TFTaModel,
										    TFTaPreTrainedModel,
										)

					try:
										if not is_flax_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_flax_ta import (
										    FlaxTaEncoderModel,
										    FlaxTaForConditionalGeneration,
										    FlaxTaModel,
										    FlaxTaPreTrainedModel,
										)


else:
					import sys

					_UpperCamelCase									=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




