





from __future__ import annotations



def A_     (		A__    )  ->		list[int]:
       a__						:     List[str]			=    [True] * limit
       a__						:     List[str]			=    False
       a__						:     List[Any]			=    False
       a__						:     str			=    True

       for i in range(3		,				int(limit**0.5 + 1    )		,				2    ):
              a__						:     str			=    i * 2
              while index < limit:
                     a__						:     Dict			=    False
                     a__						:     Tuple			=    index + i

       a__						:     Optional[Any]			=    [2]

       for i in range(3		,				A__		,				2    ):
              if is_prime[i]:
                     primes.append(A__    )

       return primes



def A_     (		A__ = 100_0000    )  ->		int:
       a__						:     Dict			=    prime_sieve(A__    )
       a__						:     Tuple			=    0
       a__						:     str			=    0

       for i in range(len(A__    )    ):
              for j in range(i + length		,				len(A__    )    ):
                     a__						:     int			=    sum(primes[i:j]    )
                     if sol >= ceiling:
                            break

                     if sol in primes:
                            a__						:     Tuple			=    j - i
                            a__						:     Union[str, Any]			=    sol

       return largest


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









from __future__ import annotations

from collections.abc import Callable



def A_     (		A__		,				A__		,				A__		,				A__ = 100		,				)  ->		float:
       a__						:     Dict			=    x_start
       a__						:     Any			=    fnc(A__    )
       a__						:     Optional[int]			=    0.0
       for _ in range(A__    ):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              a__						:     Union[str, Any]			=    (x_end - x_start) / steps + xa
              a__						:     str			=    fnc(A__    )
              area += abs(fxa + fxa    ) * (xa - xa) / 2
              # Increment step
              a__						:     Optional[Any]			=    xa
              a__						:     Optional[int]			=    fxa
       return area


if __name__ == "__main__":



    def A_     (		A__    )  ->		List[str]:
           return x**3 + x**2

    print("""f(x) = x^3 + x^2""")
    print("""The area between the curve, x = -5, x = 5 and the x axis is:""")
    lowercase				:	Union[str, Any]      						=  1_0
    while i <= 1_0_0_0_0_0:
        print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
        i *= 1_0


