Connect aruino to

There is any way to send e.g. 3+3 from arduino to and see result on LCD 16x2 screen?

Yes, it is possible but you will need either ethernet, wifi or 3G shield/breakout. Whichever one of these you choose should have an example sketch which shows using it as a HTTP client.

Have a look at the WolframAlpha site in a browser like Chrome with developer tools turned on (F12). If you go to the network tab, you will see the HTTP requests that your browser is making when you enter a calculation into the field on the page. You need to replicate that same request in your Arduino code.

One problem you may face is that you are going to get a lot of HTML back as the response, which you need to parse to find the bit that you are interested in which I assume is the answer. The Arduino doesn’t have a lot of memory, so you won’t be able to read the entire page into memory and then start parsing it - you will need to parse as you read the response and throw away the bits that you don’t want.

It would be simpler if they published an API, which would have a more compact response aimed at code rather than humans, but I didn’t see anything on their site.