


'''simple docstring'''
from collections.abc import Callable

import numpy as np





def    a__			(   lowerCAmelCase__    ,   lowerCAmelCase__    ,   lowerCAmelCase__    ,   lowerCAmelCase__    ,   lowerCAmelCase__		)       ->      np.ndarray:
    UpperCAmelCase__     :						List[Any]						=							int(np.ceil((x_end - xa) / step_size		)		)
    UpperCAmelCase__     :						Optional[Any]						=							np.zeros((n + 1,)		)
    UpperCAmelCase__     :						List[Any]						=							ya
    UpperCAmelCase__     :						Optional[int]						=							xa

    for k in range(lowerCAmelCase__		):
        UpperCAmelCase__     :						List[str]						=							y[k] + step_size * ode_func(lowerCAmelCase__    ,   y[k]		)
        x += step_size

    return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()

'''simple docstring'''




import os
from distutils.util import strtobool






def 							snake_case__				(     _A:   int ,  _A:   List[Any]					)       ->      Union[str, Any]:

		'''simple docstring'''


		for e in env_keys:
				lowerCAmelCase     =    int(os.environ.get(_A ,  -1					)					)
				if val >= 0:
						return val
		return default






def 							snake_case__				(     _A:   str ,  _A:   List[Any]=False					)       ->      int:

		'''simple docstring'''


		lowerCAmelCase     =    os.environ.get(_A ,  str(_A					)					)
		return strtobool(_A					) == 1  # As its name indicates `strtobool` actually returns an int...






def 							snake_case__				(     _A:   Dict ,  _A:   List[Any]="no"					)       ->      str:

		'''simple docstring'''


		lowerCAmelCase     =    os.environ.get(_A ,  str(_A					)					)
		return value




