What to do to avoid the numerical calculation error, shown in the example?

Hi F.M. What to do? Can do this some things:

Use VPA (Variable Precision Arithmetic). For this is why any numerical software must to have some symbolic habilitates. Above image is from Maple 11, which also gives poor numerical answers. Inputs with a dot, like 0.001 tells to maple to do numerics. But if not, maple uses symbolics and give the exact answer (where can see from where the "surprise, surprise" came :-). VPA is that you can change Digits to any number.

Use another tactic, like Multi Precision Floating Point Computing. Original site is down. Here a copy for macros for handle this calculus without symoblics: Software per Calcolo Numerico

Best regards.

Alvaro.