Python Numerical Integrator

#Python numerical integrator
import multiprocessing as mp
import time

start_time = time.time()

def f(x):
    return x**2

def integral(a, b, num, output):
    area = 0
    index = a #start at the left endpoint
    interval = 1/num
    while index < b:
        area += f(index) * interval
        index += interval
    output.put(area) #return the area back to the parent program

start = 1
end = 4
num_rectangles = 10000000

#number of independant processes to run
num_processes = 100
# Setup a list of processes that we want to run
processes = []
# Define an output queue
output = mp.Queue()

for i in range(num_processes):
    sub_a = ((end - start) / float(num_processes)) * i + start
    sub_b = sub_a + ((end - start) / float(num_processes))
    sub_num = num_rectangles / num_processes
    processes.append(mp.Process(target=integral, args=(sub_a, sub_b, sub_num, output)))

# Run processes
for p in processes:
    p.start()

# Exit the completed processes
for p in processes:
    p.join()

# Get process results from the output queue
results = sum(output.get() for p in processes)
print("Area %s" %(results))

print ("elapsed time: %s seconds" %(round(time.time() - start_time, 3)))

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