

'''simple docstring'''



from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available







@dataclass
# Copied from diffusers.pipelines.stable_diffusion.__init__.StableDiffusionPipelineOutput with Stable->Alt
class 		lowerCAmelCase__     (   a      ):



 """simple docstring"""



 lowerCAmelCase__						      =   42
 lowerCAmelCase__						      =   42


if is_transformers_available() and is_torch_available():
  from .modeling_roberta_series import RobertaSeriesModelWithTransformation
  from .pipeline_alt_diffusion import AltDiffusionPipeline
  from .pipeline_alt_diffusion_imgaimg import AltDiffusionImgaImgPipeline









'''simple docstring'''



from __future__ import annotations

from collections.abc import Callable







def      a__ (						a__   ,					a__   ,					a__   ,					a__ = 1_00   ,					):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE						     =   x_start
     __SCREAMING_SNAKE_CASE						     =   fnc(a__		)
     __SCREAMING_SNAKE_CASE						     =   0.0

     for _ in range(a__		):
          # Approximates small segments of curve as linear and solve
          # for trapezoidal area
          __SCREAMING_SNAKE_CASE						     =   (x_end - x_start) / steps + xa
          __SCREAMING_SNAKE_CASE						     =   fnc(a__		)
          area += abs(fxa + fxa		) * (xa - xa) / 2

          # Increment step
          __SCREAMING_SNAKE_CASE						     =   xa
          __SCREAMING_SNAKE_CASE						     =   fxa
     return area


if __name__ == "__main__":







  def      a__ (						a__		):




       """simple docstring"""


       return x**3

  print('f(x) = x^3')
  print('The area between the curve, x = -10, x = 10 and the x axis is:')
  UpperCAmelCase				: Optional[Any]         =  1_0
  while i <= 1_0_0_0_0_0:
    UpperCAmelCase				: Union[str, Any]         =  trapezoidal_area(f, -5, 5, i)
    print(f"""with {i} steps: {area}""")
    i *= 1_0






