Thanks to Ger, Bernard and Mark for your quick response to my question. I have looked into the options you provided and considered the pros and cons of those options. I have come down to the choice of jpgraph for the following reasons:
My selection criteria:
(2) A good range of maths functions
(3) Flexibility online capability
(4) Good technical support
(5) Able to be integrated in moodle.
(6) Good graphics quality
(7) User control
Both Maple and Mathematica are top range products and expensive. To some extent, I only need a fraction of the product features. I have no idea how easy it is to integrate them in moodle for online interaction.
I was surprised when I followed through jpGraph websites by its application flexibility and on-the-fly features. It seems to me at this stage from reading the available information on the websites jpGraph could meet most of the above selection criteria. By the way, jpgraph can be free, depending on the usage conditions.
I hope next to work out how to integrate jpgraph in moodle. If anyone has done this before (Bernard please again!) could you suggest the effective ways of integrating this maths library in moodle to allow interaction between learners and moodle? To achieve some simple user interaction I think it would need user data entry via browser to pass the input data to mySQL and jpgraph PHP library for processing and finally graphical generation. Any thoughts are welcome!