F left_rect((Float -> Float) f, Float x, Float h) -> Float
   R f(x)

F mid_rect((Float -> Float) f, Float x, Float h) -> Float
   R f(x + h / 2)

F right_rect((Float -> Float) f, Float x, Float h) -> Float
   R f(x + h)

F trapezium((Float -> Float) f, Float x, Float h) -> Float
   R (f(x) + f(x + h)) / 2.0

F simpson((Float -> Float) f, Float x, Float h) -> Float
   R (f(x) + 4 * f(x + h / 2) + f(x + h)) / 6.0

F cube(Float x) -> Float
   R x * x * x

F reciprocal(Float x) -> Float
   R 1 / x

F identity(Float x) -> Float
   R x

F integrate(f, a, b, steps, meth)
   V h = (b - a) / steps
   V ival = h * sum((0 .< steps).map(i -> @meth(@f, @a + i * @h, @h)))
   R ival

L(a, b, steps, func, func_name) [(0.0, 1.0, 100, cube, ‘cube’),
                                 (1.0, 100.0, 1000, reciprocal, ‘reciprocal’),
                                 (0.0, 5000.0, 5'000'000, identity, ‘identity’),
                                 (0.0, 6000.0, 6'000'000, identity, ‘identity’)]
   L(rule, rule_name) [(left_rect,  ‘left_rect’),
                        (mid_rect,   ‘mid_rect’),
                      (right_rect, ‘right_rect’),
                       (trapezium,  ‘trapezium’),
                         (simpson,    ‘simpson’)]
      print("#. integrated using #.\n  from #. to #. (#. steps) = #.".format(
            func_name, rule_name, a, b, steps, integrate(func, a, b, steps, rule)))