Let for $$x \in \mathbb{R}, S_{0}(x)=x, S_{k}(x)=C_{k} x+k \int_{0}^{x} S_{k-1}(t) d t$$, where

$$C_{0}=1, C_{k}=1-\int_{0}^{1} S_{k-1}(x) d x, k=1,2,3, \ldots$$ Then $$S_{2}(3)+6 C_{3}$$ is equal to ____________.

If $$\int_\limits{-0.15}^{0.15}\left|100 x^{2}-1\right| d x=\frac{k}{3000}$$, then $$k$$ is equal to ___________.

For $$m, n > 0$$, let $$\alpha(m, n)=\int_\limits{0}^{2} t^{m}(1+3 t)^{n} d t$$. If $$11 \alpha(10,6)+18 \alpha(11,5)=p(14)^{6}$$, then $$p$$ is equal to ___________.

Let $$[t]$$ denote the greatest integer function. If $$\int_\limits{0}^{2.4}\left[x^{2}\right] d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}$$, then $$\alpha+\beta+\gamma+\delta$$ is equal to __________.