Ok, this is gonna be a bit of a mixed bag. Some of these are only mellow at the beginning for the first minute or so. Others are mellow all the way through until it gets intense at the end, and others do a bit of back and forth, only to crank the intensity way up at the end.

Anyways:

Stairway To Heaven - Led Zeppelin (ok this one isn't necessarily "intense" or "angry" but the Guitar Solo and Final Verse definitely have way more energy than the rest of the song)

One - Metallica

Fade To Black- Metallica

Welcome Home (Sanitarium) - Metallica

So Far Away - Avenged Sevenfold

Gunslinger - Avenged Sevenfold

Buried Alive - Avenged Sevenfold

Cemetery Gates - Pantera (tho the intensity does drop in the last verse)

Foundations of Decay - My Chemical Romance (same thing with Cemetery Gates)

Fear of the Dark - Iron Maiden

Hallowed Be Thy Name - Iron Maiden

Don't Talk To Strangers - Dio