The function $~f~$ is continuous on its domain. In terms of $~k\,$, certain function values are given in the table below. $x$|$-3$|$0$|$3$|$6$|$9$ :-:|:-:|:-:|:-:|:-:|:-:|:-:| $f(x)$|$~~4~~$|$2k+1$|$4k-2$|$~~~k~~~$|$~~~4~~~$ If the trapezoid approximation of $~\displaystyle \int_{-3}^{9}f(x)\,dx~$ with four equal sub-intervals $~T(4)=30\,$, then what is the value of $~k\,$? $\qquad k=~$ [[☃ input-number 1]]