The given series can be written as:

S = (-1) + (-2) + (-3) + (4) + (5) + (6) + (-7) + (-8) + (-9) + (10) + (11) + (12) - ... - (175) - (176) - (177) + (178) + (179) + (180) + (181) + (182)

We can group the terms in pairs as follows:

S = [(-1) + (-2)] + [(-3) + (4)] + [(5) + (6)] + [(-7) + (-8)] + [(-9) + (10)] + [(11) + (12)] - ... - [(175) + (176)] - [(177) + (178)] + [(179) + (180)] + [(181) + (182)]

Simplifying each pair, we get:

S = -3 + 1 + 11 - 15 + 1 + 23 - ... - 351 + 359 + 359 + 363

Now, we can see that every pair of terms cancels each other out, except for the last two terms:

S = -3 + 1 + 11 - 15 + 1 + 23 - ... - 351 + 359 + 359 + 363
= -3 + 1 + 11 - 15 + 1 + 23 - ... - 351 + 359 + 722

Therefore, the sum of the given series is 722.