The documentation currently says:
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R.PNBINOM: cumulative distribution function of the negative binomial distribution

Arguments:
x: observation
n: the number of trials
psuc: the probability of success in each trial
lower_tail: if true (the default), the lower tail of the distribution is considered
log_p: if true, log of the probability is used
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Since the number of trials for the negative binomial distribution is not fixed (in fact the random variable x is the number of trials), n is not correct. In the R documentation we have: 

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Usage

dnbinom(x, size, prob, mu, log = FALSE)
pnbinom(q, size, prob, mu, lower.tail = TRUE, log.p = FALSE)
qnbinom(p, size, prob, mu, lower.tail = TRUE, log.p = FALSE)
rnbinom(n, size, prob, mu)

Arguments
x 	vector of (non-negative integer) quantiles.
q 	vector of quantiles.
p 	vector of probabilities.
n 	number of observations. If length(n) > 1, the length is taken to be the number required.
size 	target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.
prob 	probability of success in each trial. 0 < prob <= 1.
mu 	alternative parametrization via mean: see ‘Details’.
log, log.p 	logical; if TRUE, probabilities p are given as log(p).
lower.tail 	logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].
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I suspect we should have:

n: target for number of successful trials