






# This is the module that test_patching.py uses to test patch_submodule()

import os  # noqa: this is just for tests
import os as renamed_os  # noqa: this is just for tests
from os import path  # noqa: this is just for tests
from os import path as renamed_path  # noqa: this is just for tests
from os.path import join  # noqa: this is just for tests
from os.path import join as renamed_join  # noqa: this is just for tests


lowerCamelCase     :							Any    =open  # noqa: we just need to have a builtin inside this module to test it properly











def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase      )			->     Any:
     # "extended trapezoidal rule"
     # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
     UpperCamelCase__      :       int	    =  (boundary[1] - boundary[0]) / steps
     UpperCamelCase__      :       Optional[Any]	    =  boundary[0]
     UpperCamelCase__      :       List[Any]	    =  boundary[1]
     UpperCamelCase__      :       List[Any]	    =  make_points(__lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )
     UpperCamelCase__      :       int	    =  0.0
     y += (h / 2.0) * f(__lowerCAmelCase      )
     for i in x_i:
          # print(i)
          y += h * f(__lowerCAmelCase      )
     y += (h / 2.0) * f(__lowerCAmelCase      )
     return y







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     List[str]:
     UpperCamelCase__      :       Optional[int]	    =  a + h
     while x < (b - h):
          yield x
          UpperCamelCase__      :       Union[str, Any]	    =  x + h







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     Any:  # enter your function here
     UpperCamelCase__      :       Dict	    =  (x - 0) * (x - 0)
     return y







def 		SCREAMING_SNAKE_CASE							( )			->     Dict:
     UpperCamelCase__      :       List[Any]	    =  0.0  # Lower bound of integration
     UpperCamelCase__      :       Tuple	    =  1.0  # Upper bound of integration
     UpperCamelCase__      :       Any	    =  1_0.0  # define number of steps or resolution
     UpperCamelCase__      :       List[str]	    =  [a, b]  # define boundary of integration
     UpperCamelCase__      :       Any	    =  method_a(__lowerCAmelCase ,   __lowerCAmelCase      )
     print(f'y = {y}'      )


if __name__ == "__main__":
 main()