x = {1,2,3}
y = {1,4,9}
f = InterpolatingFunction.Spline(x,y)

f(2.5) -- evaluates f at 2.5
n = 1
f(2.5,n) --evaluates the n-th derivative of f at 2.5

f({1.2,2.5,2.7,2.9}) -- evaluates f successively at the given values

y2 = {2,1,2}
g = InterpolatingFunction.Spline(x,y2)
y3 = {2,4,18}      -- this equals y * y2

-- Arithmetics:
f + g
f - g

FtimesG = InterpolatingFunction.Spline(x,y2)
print(FtimesG == f * g)    -- these functions are equal

f^3 == f*f*f

f..g     -- concatenation; let X be a subset of the interval on which g is defined, when evaluating f..g on X make sure that f is defined on the image g(X), otherwise you'll get an error

InterpolatingFunction.Integrate(f) -- integrates f over its full domain
a = 1.5
b = 2.5
InterpolatingFunction.Integrate(f,a,b) -- integrates f from a to b