




import random

from .binary_exp_mod import bin_exp_mod







def 			lowerCamelCase_		(       UpperCamelCase__				:      Tuple ,     UpperCamelCase__				:      Optional[Any]=1000      )     ->       List[str]:





				"""simple docstring"""


				if n < 2:
								return False

				if n % 2 == 0:
								return n == 2

				# this means n is odd
				__lowerCamelCase		       =    n - 1
				__lowerCamelCase		       =    0
				while d % 2 == 0:
								d /= 2
								exp += 1

				# n - 1=d*(2**exp)
				__lowerCamelCase		       =    0
				while count < prec:
								__lowerCamelCase		       =    random.randint(2 ,     n - 1      )
								__lowerCamelCase		       =    bin_exp_mod(_SCREAMING_SNAKE_CASE ,     _SCREAMING_SNAKE_CASE ,     _SCREAMING_SNAKE_CASE      )
								if b != 1:
												__lowerCamelCase		       =    True
												for _ in range(_SCREAMING_SNAKE_CASE      ):
																if b == n - 1:
																				__lowerCamelCase		       =    False
																				break
																__lowerCamelCase		       =    b * b
																b %= n
												if flag:
																return False
												count += 1
				return True


if __name__ == "__main__":
					__A        =    abs(int(input("Enter bound : ").strip()))
					print("Here\'s the list of primes:")
					print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))








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

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       lowerCamelCase   :      int			 =					a + h
       while x < (b - h):
              yield x
              lowerCamelCase   :      List[str]			 =					x + h

def      A      (      _SCREAMING_SNAKE_CASE    )	-> Optional[Any]:  # enter your function here
       lowerCamelCase   :      str			 =					(x - 0) * (x - 0)
       return y

def      A      (      )	-> int:
       lowerCamelCase   :      int			 =					0.0  # Lower bound of integration
       lowerCamelCase   :      int			 =					1.0  # Upper bound of integration
       lowerCamelCase   :      Dict			 =					10.0  # define number of steps or resolution
       lowerCamelCase   :      int			 =					[a, b]  # define boundary of integration
       lowerCamelCase   :      str			 =					method_a(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       print(f'''y = {y}'''    )


if __name__ == "__main__":
       main()






