

'''simple docstring'''







from __future__ import annotations

from collections.abc import Callable
def       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__ = 1_00,       )			->			float:
       A_						=      x_start
       A_						=      fnc(UpperCAmelCase__				)
       A_						=      0.0
       for _ in range(UpperCAmelCase__				):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              A_						=      (x_end - x_start) / steps + xa
              A_						=      fnc(UpperCAmelCase__				)
              area += abs(fxa + fxa				) * (xa - xa) / 2
              # Increment step
              A_						=      xa
              A_						=      fxa
       return area


if __name__ == "__main__":
      def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			Any:
             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:''')
      __lowerCamelCase		       =    10
      while i <= 10_0000:
            print(f"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
            i *= 10



'''simple docstring'''







from __future__ import annotations

import math
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			bool:

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5,       int(math.sqrt(UpperCAmelCase__				) + 1				),       6				):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True


__lowerCamelCase		       =    [num for num in range(3, 10_0001, 2) if not is_prime(num)]
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			list[int]:
       if not isinstance(UpperCAmelCase__,       UpperCAmelCase__				):
              raise ValueError("""n must be an integer"""				)
       if n <= 0:
              raise ValueError("""n must be >= 0"""				)

       A_						=      []
       for num in range(len(UpperCAmelCase__				)				):
              A_						=      0
              while 2 * i * i <= odd_composites[num]:
                     A_						=      odd_composites[num] - 2 * i * i
                     if is_prime(UpperCAmelCase__				):
                            break
                     i += 1
              else:
                     list_nums.append(odd_composites[num]				)
                     if len(UpperCAmelCase__				) == n:
                            return list_nums

       return []
def       UpperCAmelCase__    (      )			->			int:
       return compute_nums(1				)[0]


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