



def 	__UpperCamelCase	(  _lowerCAmelCase      ,     _lowerCAmelCase		)       ->  Tuple:



    """simple docstring"""






    A :       List[Any]          =   (boundary[1] - boundary[0]) / steps
    A :       Any          =   boundary[0]
    A :       str          =   boundary[1]
    A :       str          =   make_points(_lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase		)
    A :       Dict          =   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 	__UpperCamelCase	(  _lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase		)       ->  Union[str, Any]:



    """simple docstring"""






    A :       List[Any]          =   a + h
    while x < (b - h):
        yield x
        A :       List[Any]          =   x + h




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  List[Any]:  # enter your function here



    """simple docstring"""






    A :       List[str]          =   (x - 0) * (x - 0)
    return y




def 	__UpperCamelCase	(  )       ->  List[str]:



    """simple docstring"""






    A :       List[str]          =   0.0  # Lower bound of integration
    A :       str          =   1.0  # Upper bound of integration
    A :       str          =   10.0  # define number of steps or resolution
    A :       int          =   [a, b]  # define boundary of integration
    A :       Tuple          =   method_a(_lowerCAmelCase      ,     _lowerCAmelCase		)
    print(f'''y = {y}'''		)


if __name__ == "__main__":
     main()







from __future__ import annotations

from math import ceil, floor, sqrt




def 	__UpperCamelCase	(  _lowerCAmelCase = 200_0000		)       ->  int:



    """simple docstring"""






    A :       list[int]          =   [0]
    A :       int

    for idx in range(1      ,     ceil(sqrt(target * 2		) * 1.1		)		):
        triangle_numbers.append(triangle_numbers[-1] + idx		)

    # we want this to be as close as possible to target
    A :       int          =   0
    # the area corresponding to the grid that gives the product closest to target
    A :       int          =   0
    # an estimate of b, using the quadratic formula
    A :       float
    # the largest integer less than b_estimate
    A :       int
    # the largest integer less than b_estimate
    A :       int
    # the triangle number corresponding to b_floor
    A :       int
    # the triangle number corresponding to b_ceil
    A :       int

    for idx_a, triangle_a in enumerate(triangle_numbers[1:]      ,     1		):
        A :       Union[str, Any]          =   (-1 + sqrt(1 + 8 * target / triangle_a		)) / 2
        A :       List[Any]          =   floor(_lowerCAmelCase		)
        A :       Tuple          =   ceil(_lowerCAmelCase		)
        A :       int          =   triangle_numbers[b_floor]
        A :       Dict          =   triangle_numbers[b_ceil]

        if abs(target - triangle_b_first_guess * triangle_a		) < abs(
            target - best_product		):
            A :       Optional[int]          =   triangle_b_first_guess * triangle_a
            A :       Optional[int]          =   idx_a * b_floor

        if abs(target - triangle_b_second_guess * triangle_a		) < abs(
            target - best_product		):
            A :       Tuple          =   triangle_b_second_guess * triangle_a
            A :       Tuple          =   idx_a * b_ceil

    return area


if __name__ == "__main__":
     print(F"""{solution() = }""")


