
"""simple docstring"""



import numpy as np


def 			_UpperCamelCase						(    _A       ,   _A       ,   _A       ,   _A       ,   _A   )     ->	Dict:





    """simple docstring"""

    _UpperCAmelCase        = int(np.ceil((x_end - xa) / h   )   )
    _UpperCAmelCase        = np.zeros((n + 1,)   )
    _UpperCAmelCase        = ya
    _UpperCAmelCase        = xa

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

    return y


if __name__ == "__main__":
 import doctest

 doctest.testmod()







"""simple docstring"""
import os
from typing import Dict, List, Tuple, TypeVar, Union


lowerCamelCase_							      = TypeVar('''T''')

lowerCamelCase_							      = Union[List[T], Tuple[T, ...]]
lowerCamelCase_							      = Union[T, List[T], Dict[str, T]]
lowerCamelCase_							      = Union[str, bytes, os.PathLike]



