Which software(s) can serve as Mathematica, Maple or MATLAB equivalents?

Octave provides a lot of the functionality of Matlab, and can run some Matlab programs. Sage is the open source "equivalent" of Mathematica.

I use QT Octave as GNU Octave does not have a nice GUI. Though most of the commands work out pretty well, some functions may not work as expected in MATLAB

You can also give R a try. It is an open-source, free, programming environment. It has both powerful visualization capabilities, power numerical libraries, and everything you would expect from a functional programming language (well, except a compiler).