




import re

from filelock import FileLock


try:
     import nltk

     UpperCamelCase								=	True
except (ImportError, ModuleNotFoundError):
     UpperCamelCase								=	False

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



def 				_A  (		lowerCAmelCase_	:   str     ):
     """simple docstring"""

     re.sub("<n>"  ,							""  ,							lowerCAmelCase_     )  # 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(lowerCAmelCase_     )     )






import numpy as np
def 		a_							( __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase				):
  lowerCAmelCase__										=      int(np.ceil((x_end - xa) / h				)				)
  lowerCAmelCase__										=      np.zeros((n + 1,)				)
  lowerCAmelCase__										=      ya
  lowerCAmelCase__										=      xa

  for k in range(__lowerCAmelCase				):
    lowerCAmelCase__										=      f(__lowerCAmelCase   , y[k]				)
    lowerCAmelCase__										=      f(x + 0.5 * h   , y[k] + 0.5 * h * ka				)
    lowerCAmelCase__										=      f(x + 0.5 * h   , y[k] + 0.5 * h * ka				)
    lowerCAmelCase__										=      f(x + h   , y[k] + h * ka				)
    lowerCAmelCase__										=      y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
    x += h

  return y


if __name__ == "__main__":
      import doctest

      doctest.testmod()

