I really enjoy doing math problems!
This fun little mystery cache should be a bit of calculus nostalgia for many of you. The savvy cacher will solve several area-under-a-curve questions. The CO intends for the solution to be derived using the concept of Integration in basic Calculus. To keep things simple, the definite integral shall be used in general and without a constant-of-integration. That said, there are many ways to derive a solution. One may use Taylor approximations, brute force calculations, summation of polygons, or physical cut-n-paste techniques, etc. The ultimate approach you choose is entirely yours to make. Have fun! Calculate those areas and get that well deserved smiley.
First, the cache is not hidden at the published location. Second, BYOP. Third, this cache is placed in a semi-secure area. The optimal time to attempt this cache is Monday through Friday from sunrise to sunset. There are several ways to approach GZ. Should you see the gate closed, come back another day. Should you approach a guard station turn left or turn right to avoid it and simply go around the long way.
What about that final stage? Well, laying your hands on the cache should be rather anti-climatic after you've spent a moment solving all of the challenges. This is intentional. You deserve a well earned break. I believe all geocachers that give this a go are not keen to toot-their-own horn nor pat themselves on the back. I genuinely embrace such humble modesty. I will be your cheerleader. You're amazing for giving this cache a try! Congratulations to all who are successful in solving the challenges and ultimately signing the log for that well deserved smiley. The final stage should be a grab & go. Beware of muggles. Look like you belong there and you will fit in.
Solve for Position-Q
Solve for Position-W
Solve for Position-E
Solve for Position-R
Solve for Position-T
Solve for Position-Y
You can check your answers for this puzzle on GeoChecker.com.