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Is there a way to have interval arithmetics for complex inputs
(maple seems to name that range arithmetics in the help)?

x:=Pi/5;
shake(x);

              INTERVAL(0.628318529462 .. 0.628318531974)

shake(x*I);

    Error, (in evalr/shake) not a real number

How can I use 'evalr' and 'shake' for functions (in a relative or absolute sense)?

What I see in the help is the result for disturbing the input to a function (by decimal digits).

But I want ranges for the output, if the function itself is disturbed, not only the input
(giving resulting error ranges, even for exact input).

Any idea?