import decimal

from decimal import *
getcontext().prec = 50

xbegin = Decimal ('0')
xeinde = Decimal ('1')
aantalstappen = 2000000
stap = (Decimal (xeinde) - Decimal (xbegin)) / Decimal (aantalstappen)

n = Decimal ('0.1')

# Dit zijn 3 stappen:
# for j in range (1, 4, 1):

# 10^5 stappen betekent 75 seconden per j
for j in range (1, 2, 1):

 n = Decimal (n) + Decimal ('0.01')
 s = Decimal ('0')
 x = Decimal (xbegin)
 fx = Decimal ('1')

 for i in range (1, aantalstappen + 1, 1):

  x = Decimal (x) + Decimal (stap)

  fxprev = Decimal (fx)
  fx = (Decimal ('1') + (Decimal (n) * Decimal (x) ** (Decimal (n) - Decimal ('1'))) ** Decimal ('2')) ** Decimal ('0.5')
  s = Decimal (s) + (Decimal (fxprev) + Decimal (fx)) * Decimal (stap) / Decimal ('2')

 print (n, s)