KBB Pricing for the 2011 Honda Civic ranges around $6,500 - $8,500. A new engine, and labor together will probably exceed $2,000.
Honestly it's up to you if you think your car is worth fixing. There's still plenty of value in it being a 2011. If you junk it as is, you might actually be losing money just to not deal with the hassle.
If the cars in poor condition already (exterior wise), then honestly it might not be worth fixing. The value of the car will degrade (like damaged body, or faded paint).
If you plan to put a new engine, obviously drop a 2010-2011 Engine (pointing out the obvious).