Develop a plot of a cubic spline fit of the following data with (a) Natural end conditions

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Develop a plot of a cubic spline fit of the following data with

(a) Natural end conditions and 

(b) Not-a-knot end conditions. In addition, develop a plot using (c) piecewise cubic Hermite interpolation.

In each case, compare your plot with the following equation which was used to generate the data:

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