
from __future__ import annotations

from typing import Any







def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   int:
       if not postfix_notation:
              return 0

       lowercase							:					Optional[int]	     =				{"""+""", """-""", """*""", """/"""}
       lowercase							:					list[Any]	     =				[]

       for token in postfix_notation:
              if token in operations:
                     lowercase     ,      lowercase							:					List[str]	     =				stack.pop(), stack.pop()
                     if token == "+":
                            stack.append(a + b    )
                     elif token == "-":
                            stack.append(a - b    )
                     elif token == "*":
                            stack.append(a * b    )
                     else:
                            if a * b < 0 and a % b != 0:
                                   stack.append(a // b + 1    )
                            else:
                                   stack.append(a // b    )
              else:
                     stack.append(int(SCREAMING_SNAKE_CASE__    )    )

       return stack.pop()


if __name__ == "__main__":
  import doctest

  doctest.testmod()


from collections.abc import Callable

import numpy as np







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   np.array:
       lowercase							:					Optional[int]	     =				int(np.ceil((x_end - xa) / step_size    )    )
       lowercase							:					List[Any]	     =				np.zeros((n + 1,)    )
       lowercase							:					Optional[int]	     =				ya
       lowercase							:					Optional[int]	     =				xa

       for k in range(SCREAMING_SNAKE_CASE__    ):
              lowercase							:					str	     =				y[k] + step_size * ode_func(SCREAMING_SNAKE_CASE__ ,     y[k]    )
              lowercase							:					Union[str, Any]	     =				y[k] + (
                  (step_size / 2) * (ode_func(SCREAMING_SNAKE_CASE__ ,     y[k]    ) + ode_func(x + step_size ,     SCREAMING_SNAKE_CASE__    ))
              )
              x += step_size

       return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()
