Bit by Bit Tool Kit

Tib's original code came from a radio transmission which he received in base 64 format. In order to learn how to find the value that Tib needs for his bit kit, we will parse the base 64 input and follow a series of steps involving ascii values and bitwise manipulation. Let's walk through an example together:

Suppose you are given the input b64 string: 'Y3Rmfnw='

The decoded version of this string is: 'ctf~|'
You may notice that the first part of the string begins with lowercase letters and has a series of bitwise operations (1 less than the amount of letters). This holds true for any transmission.

First, we need to take the ascii values of each letter and cube it. This gives us our number sequence which will be used later. In our example (^ means exponent, not XOR): c = 99^3 = 970299, t = 116^3 = 1560896, and f = 102^3 = 1061208.

Next, we set our starting value to the first number in the sequence (970299 in this case). Using that value as the first operand, we will each bitwise operation on subsequent numbers in our number set. If the bitwise operation is unary (~), it is applied to the current value, and the next number is skipped. Once we go through all of the bitwise operations, we use the result as the next starting value, and the starting position for both the numbers and bitwise operations increases by 1. This is how the tool kit is used in our example:
(v: the value as a result of the operation)
initial v = 970299
v = ~970299 = -970300 (skip t because ~ is unary)
v = -970300 | 1061208 = -970276
(starting position increases, keep resulting value)
v = -970276 | 1061208 = -970276
(all operations complete in sequence)
Result: -970276

Here is another example using a longer input. The variables have a number appended to them which represents the corresponding number, operation, or value.
Input: 'bGVtb24mJn4+Pg==' --> 'lemon>>^|&'
Letter values: l = 1259712, e = 1030301, m = 1295029, o = 1367631, n = 1331000
Operations: >>, ^, |, &

V0 = l
V1 = V0 >> e
V2 = V1 ^ m
V3 = V2 | o
V4 = V3 & n
New starting value: V0 = V4 (1330744)
V1 = V0 ^ m
V2 = V1 | o
V3 = V2 & n
New starting value: V0 = V3 (1330696)
V1 = V0 | o
V2 = V1 & n
New starting value: V0 = V2 (1330696)
V1 = V0 & n (final operation)
Result: 1330696

Now go and help Tib, he's about to lose it!

[Additional Test Cases]
Base64 --> Value
=====================
YWxiYXRyb3Nzfl4mfH58Xnw= --> -1
Y3RmbGVhcm5ePj5+Pj5+Pj58 --> 1331000
c3BhZ2hldHRpJj4+fn58fl4m --> 10393
aWJldHlvdWp1c3R0cmllZHRoaXNiZWNhdXNleW91d2FudGVkdG9rbm93d2hhdHRoZW1lc3NhZ2V3YXNeXj4+Xl4mfD4+fCZ8Pj4+PiZePj5+Pj5ePj5ePj4+Pj4+fj4+Pj58fiZ8fCZ8fH4+Pn4+Pn5efH5efl58fCZ8Pj5+Pj5+Pj58JiY= --> 74785