There are four ways to evaluate the expression " $\pm 2 \pm 5$ ":

$$
2+5=7 \quad 2-5=-3 \quad-2+5=3 \quad-2-5=-7
$$

There are eight ways to evaluate the expression " $\pm 2^{11} \pm 2^{5} \pm 2$ ". When these eight values are listed in decreasing order, what is the third value in the list?
Since $2^{11}=2048$ and $2^{5}=32$, the eight values are

$$
\begin{aligned}
& 2^{11}+2^{5}+2=2082 \quad 2^{11}+2^{5}-2=2078 \quad 2^{11}-2^{5}+2=2018 \quad 2^{11}-2^{5}-2=2014 \\
& -2^{11}+2^{5}+2=-2014-2^{11}+2^{5}-2=-2018 \quad-2^{11}-2^{5}+2=-2078 \quad-2^{11}-2^{5}-2=-2082
\end{aligned}
$$

The third largest value is $2^{11}-2^{5}+2=2018$.

ANSWER: $2^{11}-2^{5}+2=2018$