The computer algebra system Maple allows to control the
rounding mode of (arbitrary precision) arithmetic operations.
As we will see, using this feature naively may result in
unexpected results. There are also situations in which
the evalr command is not faithful to the power set model
for interval arithmetic.
However, the interval package intpakX (available as a
Maple Power Tool since 2002) may be used to perform
arbitrary precision interval operations in a safe way.
In the first part of the talk we give a summary
of the most interesting features supported by intpakX.
The second part we show how symbolic-numeric
computations may be used to solve several sample problems
with guaranteed results (the computed results may be interpreted
as computer-assisted proofs of mathematical properties of
the problems under consideration).
Different approaches to the reliable computation of orbits
of a chaotic dynamical system will be discussed in some detail.