



from __future__ import annotations

from math import pi, pow

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

def  a_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase ,_lowerCAmelCase )   ->   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 ) )

  __lowerCamelCase : Optional[int]					 =				(
      (radius_a - radius_a + centers_distance)
      * (radius_a + radius_a - centers_distance)
      / (2 * centers_distance)
  )
  __lowerCamelCase : Any					 =				(
      (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  a_  (							_lowerCAmelCase ,_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase ,_lowerCAmelCase )   ->   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_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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_  (							_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							_lowerCAmelCase ,_lowerCAmelCase )   ->   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  a_  (							)   ->   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'''





import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
   import torch

   from transformers import CamembertModel






@require_torch
@require_sentencepiece
@require_tokenizers
class       lowerCamelCase_					(       unittest.TestCase  ):
  """simple docstring"""




  @slow
  def 		_lowercase  (				self   :			str     )      ->      List[Any]:
    __lowerCamelCase : str					 =				CamembertModel.from_pretrained('camembert-base'     )
    model.to(_a     )

    __lowerCamelCase : List[Any]					 =				torch.tensor(
        [[5, 121, 11, 660, 16, 730, 2_5543, 110, 83, 6]]    ,			device=_a    ,			dtype=torch.long    ,			)  # J'aime le camembert !
    with torch.no_grad():
      __lowerCamelCase : int					 =				model(_a     )['last_hidden_state']
    __lowerCamelCase : Optional[int]					 =				torch.Size((1, 10, 768)     )
    self.assertEqual(output.shape    ,			_a     )
    # compare the actual values for a slice.
    __lowerCamelCase : Tuple					 =				torch.tensor(
        [[[-0.0254, 0.0235, 0.1027], [0.0606, -0.1811, -0.0418], [-0.1561, -0.1127, 0.2687]]]    ,			device=_a    ,			dtype=torch.float    ,			)
    # camembert = torch.hub.load('pytorch/fairseq', 'camembert.v0')
    # camembert.eval()
    # expected_slice = roberta.model.forward(input_ids)[0][:, :3, :3].detach()

    self.assertTrue(torch.allclose(output[:, :3, :3]    ,			_a    ,			atol=1e-4     )     )






