If you mean the one that TWC assigns you, it's kind of easy.
Connect your computer directly to the modem is it isn't already.
Open a command prompt, and type in IPCONFIG /RELEASE (lower case)
That will release the modem and IP address.
If you have a router, get into it's settings, and assign a new MAC address,
there should be a place to do that.
Once THAT is done, power off the router, connect it to the modem,
and then power it back on.
As it connects, it will get a new IP adress.
If you aren't using a router, you should consider getting one.
Otherwise, you'll have to change the MAC address in your computer,
and that can be more difficult, and depends on your specific make and model.
That's an 8717 which is an all in one modem/ router advanced gateway...
unless you put it in bridged mode, you can't get a downstream device to cause the public IP to change in NAT
This topic is mostly answered, but I wish to add a little FYI.
Your external IP address (click) is assigned by TWC's CMTS server for your area.
Residential TWC data customers get a dynamic IP (changes periodically)
Commerical TWC data customers can pay to get a static IP address.
It used to be the residential customers could pay extra to have additional IP address(es) and pay for static IP address(es), but not anymore. At least not in any market I know of.
What you do with your own LAN IP addresses is up to your switching device (usually a router) and its firmware options (some are more sophisticated than others). If it's a private LAN (i.e.: your own privately owned router), TWC should be strongly avoiding messing with private (non-TWC) LAN settings at all, as that's veturing into PC repair territory. For example, I've had to tell more than a few customers a form of "no" when it comes to removing malware on their PC. I know quite well from past work experience how to help with that myself but
A) that sets the bar high for my colleagues who don't know how to do that, sets then up to fail at the customer's expectations for something they weren't trained for
B) TWC is supposed to be acting more like utility/connections company, and doing things outside of our scope of work opens the company up to damages claims (even frivalous ones).
Actually your external IP address assigned by TW can stay the same no matter how many times you release the IP address and ask for a renewal. The Server uses a database to keep track of the mac addresses of the hardware that is connected to the modem, be it a router or your computer directly. There is a way to change your ip address you can clone you computer mac address onto your router to get a new wan ip address, but there should be no reason you would want to unless someone.server has banned you, or you are getting flooded by ddoser. Good luck.