I started out with an Elite Fleet Plasma-Integrated Warp core mk xii [amp] [eff] [ssr] [w->e] [wcap] from the fleet spire. In its original form, it gave the promised bonus power to engines.
After upgrading to epic Elite Fleet Plasma-Integrated Warp core mk xiv [amp] [eff] [ssr] [w->e] [w->s] [wcap] I lost the engines bonus, but got the shield one.
When in orbit space or a combat zone, I had 38 shield power and 43 engines without the core. Putting the core on bumped the shields to 48 but had no effect on the engine power.
Character is Angros - I have screen shots, but don't see a way to upload them. Also submitted a ticket via arc account, but reply said it wouldn't be addressed from that system. Will submit in game bug report tomorrow.
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