




from __future__ import annotations

from collections.abc import Callable



def   lowerCAmelCase						(						_lowerCAmelCase							:      Callable[[int | float], int | float]  ,							_lowerCAmelCase							:      int | float  ,							_lowerCAmelCase							:      int | float  ,							_lowerCAmelCase							:      int = 100  ,							):




 """simple docstring"""







 UpperCAmelCase__							       =  x_start
 UpperCAmelCase__							       =  fnc(__UpperCAmelCase		)
 UpperCAmelCase__							       =  0.0
 for _ in range(__UpperCAmelCase		):
  # Approximates small segments of curve as linear and solve
  # for trapezoidal area
  UpperCAmelCase__							       =  (x_end - x_start) / steps + xa
  UpperCAmelCase__							       =  fnc(__UpperCAmelCase		)
  area += abs(fxa + fxa		) * (xa - xa) / 2
  # Increment step
  UpperCAmelCase__							       =  xa
  UpperCAmelCase__							       =  fxa
 return area


if __name__ == "__main__":



  def   lowerCAmelCase						(						_lowerCAmelCase							:      str		):




   """simple docstring"""







   return x**3 + x**2

  print("f(x) = x^3 + x^2")
  print("The area between the curve, x = -5, x = 5 and the x axis is:")
  _lowerCAmelCase  :      List[Any]						=      1_0
  while i <= 1_0_0_0_0_0:
    print(F'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
    i *= 1_0











import re

from filelock import FileLock


try:
   import nltk

   lowerCamelCase__ :   str					=							True
except (ImportError, ModuleNotFoundError):
   lowerCamelCase__ :   Union[str, Any]					=							False

if NLTK_AVAILABLE:
   with FileLock('.lock') as lock:
      nltk.download('punkt', quiet=True)

def 					UpperCAmelCase_							(      __UpperCAmelCase						:	str							)					-> str:
      re.sub('<n>'			,			''			,			__UpperCAmelCase							)  # remove pegasus newline char
      assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
      return "\n".join(nltk.sent_tokenize(__UpperCAmelCase							)							)