#!/usr/bin/ruby
# from Dominik Geisel

include Math

def f(f,x)
 eval(f)
end

print "enter function (example sin(x): "
formula = STDIN.gets.chomp

print "first border: "
a = STDIN.gets.chomp.to_f

print "second border: "
b = STDIN.gets.chomp.to_f

print "number of intervals: "
intervals = STDIN.gets.chomp.to_i

n = intervals / 2
h = (b - a) / (2 * n)

print "\nlength of one interval: ",h,"\n"

# fill an array with the function values on (a + step)
array = [f(formula,a)]
while a <= b
 a = a + h
 array = array + [f(formula,a)]
end

# get even sum
i = 2
evensum = 0
while i < intervals
 evensum = evensum + array[i]
 i = i+2
end

# get odd sum
i = 1
oddsum = 0
while i < intervals
 oddsum = oddsum + array[i]
i = i+2
end

# calculate the integral
integral = h/3 * ( array[0] + array[intervals] + (2*evensum) + (4*oddsum) )

print "Integral: ",integral,"\n"