AOC.hs

import Text.Printf (printf)

-- (n,p,d) represents coefficient, power, denominator of a algebric term. 
-- (4,2,3) == 4 * (x ^ 2) /3
-- f(x) == n1 * (x ^ p1) / d1   +   n2 * (x ^ p2) / d2 ....

-- integrates f(x)
integrate l = [(n,p+1,(p+1)*d) | (n,p,d) <- l]

-- squares a function - f^2(x)
-- f(x) = (x+1)
-- f^2(x) = (x+1)^2
sq l = [(n*n', p+p', d*d') | (n,p,d) <- l, (n',p',d') <- l ]

-- evaluates the expr for a value
solve_ l v = sum ([( fromIntegral  n)*(( fromIntegral v)^p) / (fromIntegral  d) | (n, p, d) <- l, p >= 0]) + ( sum [( fromIntegral  n)/(( fromIntegral v)^(-p) * (fromIntegral  d)) | (n, p, d) <- l, p < 0])



solve :: Int -> Int -> [Int] -> [Int] -> [Double]
solve l r a b  
    | otherwise = [area, vol]
    where 
        c = [1,1 ..]
        f = zip3 a b c

        f_area = integrate f
        f_volume = integrate $ sq f

        area = (solve_ f_area r) - (solve_ f_area l)
        vol = pi *  ((solve_ f_volume  r) - (solve_ f_volume  l))

main :: IO ()
main = getContents >>= mapM_ (printf "%.1f\n"). (\[a, b, [l, r]] -> solve l r a b). map (map read. words). lines