Engine replacement costs more than the car's value

The Kelley Blue Book value is around $2,700-$3,700. The engine of the car died while driving down the highway. The AAA service center said the engine will need to be replaced, at a cost of around $4,100.00. I had it towed to a Toyota dealership for a second opinion, and they too have said the engine will need to be replaced. They will charge around $6,200.00.

My dilemma is this, since the cost of replacing the engine is more than the Kelley Blue Book value of the car, is this worth doing?
On the one hand I hear that Toyota's can go 200,000 miles, and this car has only 80,000 miles on it. So it might actually have a lot of life left in it.
On the other hand mileage is different from age. This car is nine years old, meaning other parts like the transmission are nine years old, even if the engine is new.

How many years do Toyota's last? Can I still get another four to five years of use from this vehicle? Or is it always a bad decision to spend more money fixing a car than the Kelley Blue Book value of the car?