This was what I tried...
wget -A rar [-r [-l 1]] <mediafireurl>
That is to say, I tried with and without the recursive option. It ends up downloading an HTML page of a few KB in size, while what I want is in the range 90-100 MB and RAR.
What happens with MediaFire for those who may not be aware, is that it first says
Processing Download Request...
This text after a second or so turns into the download link and reads
Click here to start download..
I would appreciate it if someone would tell me how to write a proper script for this situation.