I'm not sure but I'm not happy with the change. I thought they did a great job of making conditional logic easy for the masses through their 'recipes'. The new applets hide what little complexity the service previously had and now its just confusing to me.

If you're on iOS (Android soon), try Stringify. Multiple ANDs/ORs/cascading actions, etc *I work for Stringify

I do not seem to be able to create a flow that when I push the button it will call some URL with certain parameters. Does that exist?

Yes - add the 'Maker' thing - it will send HTTP GET/POST/PUT.

Or Triggi (www.triggi.com) . Direct competitor to Stringify from the NL. Disclaimer: I work there as Creative Technologist

is there going to be a web version?

Android first, then we'll look at web.

The change in the service is a direct reflection on their best guess at how to best answer the return on investments they have taken. These changes rarely benefit the customer's pocketbook, or at least IFTTT's version of a given customer's pocketbook.