Here it is: Deep Thought's ultimate helper program for first-year Calculus. There are six functions in total: tangent line finder, approximate differentiation, approximate integration, slope field, Euler's method calculator, and Newton's method calculator. The tangent line finder prompts for any function with regard to X, then asks for the X-value at which to find the tangent, which it displays in Y=mX+b form. The approximate differentiation function asks for a function for which to find the d/dx derivative, then asks for the value at which to do it, displaying the answer as Y'(X). The approximate integration function is much more advanced, asking for a function to integrate in a convenient mathprint mode, then asking for the limits of integration (a and b, in that order). Finally, it asks for the number of divisions. This is necessary to calculate the Riemann sum, but even if you're using the function to find the exact value of the integral, the arc length, or the average value, you should still type a number of divisions (try 1 in that case to make it faster). It displays the boxes that you'd use if you were making a Riemann sum by hand. To skip this step, press any key while it's drawing the boxes. Finally, it displays the values for the Riemann left, right, midpoint, trapezoid, and Simpson's rules, as well as the actual value, the arc length, and the average value (you may have to wait a bit longer for the last two). The slope field drawer asks for a differential function in terms of X and Y, then the window range. Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl are exactly the same as when using window range for any Y-function. It draws the slope field, then pauses. If you wish to save the picture, instead of pressing ENTER, which clears the graph and goes back to the program, you should break the program by pressing CLEAR, then saving the picture by StorePic. The Euler's Method calculator similarly asks for a X-Y differential function, but then asks for the Xmin (the initial X-value), Xmax (the final X-value at which to find the Y-value), Y(Xmin) (the initial Y-value), and step size. It gives a quick graph of the lines drawn, then displays a paused screen reminding the user of the functions for X and Y, and finally, after the user presses ENTER, displays a table. This may look somewhat complex at first, but it really is quite simple: the table is already scrolled to the value you asked. Check u(n) for the X-value, and v(n) for the Y-value. To scroll the table, make sure the cursor is in the n column, then press up or down to scroll. Newton's method works similarly, except that it first prompts for a classic function in terms of X, then the Y-value to match it to (where you should enter 0 if you're finding roots), then the initial X-value, then the number of approximations.