Hirasawa Susumu. This composer has written the soundtracks to anime like
Berserk,
Millennium Actress, and
Paranoia Agent; his music falls squarely within the realm of electronica and has a very distinctive style.
The Black Mages perform rock versions of Final Fantasy music, with more of an emphasis on high-octane pieces like battle music than on the slower or more atmospheric tracks. Nobuo Uematsu himself is a founding member of the band, which is one of the main reasons why they are so awesome.
Quite a few of the songs I know of that match your description are anime songs, like
“True” (sung by Shimokawa Mikuni) from some anime called Dragon Drive and
“You Get to Burning” (sung by Matsuzawa Yuumi) from the Nadesico OST. For a complete album, The Gundam Seed Destiny Complete Best album is composed songs by a variety of J-pop and J-rock artists, most of which are high-energy and have a bit of an electric feel to them (examples:
“Ignited” by T.M. Revolution and
“Life Goes On” by Arisaka Mika).
You also might like
“Inner Universe” and
“Rise” from Ghost in the Shell: SAC, both of which are composed by Kanno Youko and sung by Origa.