Thanks, Nexxo. I think I understand what you're saying in your post. After so many days since I downloaded and installed WinRAR, those pop-up messages would start appearing, telling me I have only xx days remaining on my 40 day free trial use.
Anyway, I found the info I was asking everyone I knew here on Civfanatics: what is the main site where a person who wants to keep WinRAR beyond the 40 day trial period by paying the $35.00 or so? I went via Wikipedia, and they have a link to the main web site. from that link, I can then pay one of those "dealers" (whatever that means) with either a bank card or PayPal.
As I don't get money in my bank account until Friday 2 March, I have to wait about 24 hours to check it out. But then I'll have WinRAR, at least for this computer, and I'll be able to download and extract both scenarios and user-made maps for CIVs III & IV (which I also own).
Thanks for the helpful post,