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.