Maple Intro 1Jeff KallenbachThis is a sample MAPLE input file that exhibits a few basic commands. The commands that I type in are preceded by a red prompt >. The blue text that appears is the output of the preceding command. Here we go. I input this text (not interpreted by the MAPLE command interpreter) by pressing on the "T" in the command palette above. When ready to enter commands, press on the [> icon. Here we go.The restart command clears all the variables. It should appear at the beginning of your MAPLE 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A simple calculator-like command can be inputQyQsKiIiJCIiIi1JIipHJSpwcm90ZWN0ZWRHNiQiIiYiIiNGJS1JIl5HRig2JCIiJUYrRiUqJEkjUGlHRihGJEYlRiU=This has a numeric value of course. You can evaluate the symbols of the previous command like this:QyQtSSZldmFsZkclKnByb3RlY3RlZEc2I0kiJUc2IiIiIg==Fractions (numbers or variables) are input naturally:QyQqJiwmKiRJInhHNiIiIiMiIiIqJEkieUdGJ0YoISIiRiksJkYmRilGK0YpRixGKQ==Obviously this fraction can be reduced:QyQtSSlzaW1wbGlmeUc2IjYjSSIlR0YlIiIiThe syntax for a square root is natural. Or, you can choose the square root from the palette at the left. Expressions for sin, cos, and e are also on that palette:QyQsJi1JJXNxcnRHNiI2IywmIiIjIiIiKiRJInhHRiZGKUYqRioqJi1JJGV4cEdGJjYjRixGKi1JJGNvc0dGJjYjLCRGLCIiJkYqRipGKg==Complex expressions can be assigned to a variable for future use. An assignment is made using a colon followed immediately by an equal sign:QyQ+SSdEaWZmU3FHNiIsJiokSSJ4R0YlIiIjIiIiKiRJInlHRiVGKSEiIkYqThat new shorthand can be used any time the expression would be:QyQsJkknRGlmZlNxRzYiIiIkIiIoIiIiRig=Commands can be combined on a line. the built-in command "factor" can be used on our expression with predictable results:QyYsJkknRGlmZlNxRzYiIiIjISIkIiIiRigtSSdmYWN0b3JHRiU2I0YkRig=Placing a colon instead of a semicolon at the end of a command suppresses the immediate output:QyQ+SShOZXdFeHByRzYiLCZJJ0RpZmZTcUdGJSIiJSEiKSIiIkYqBut the command was executed, so the new variable contains what it should:QyRJKE5ld0V4cHJHNiIiIiI=Maple can solve, differentiate, and integrate expressions naturally. Make sure you know what the syntax means in each case:QyQ+SS1OZXdRdWFkcmF0aWNHNiIsKCokSSJ4R0YlIiIjIiIiRighIiMhIiRGKkYqQyQtSSZzb2x2ZUc2IjYkL0ktTmV3UXVhZHJhdGljR0YlIiIhSSJ4R0YlIiIiQyQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkSS1OZXdRdWFkcmF0aWNHNiJJInhHRigiIiI=QyQtSSRpbnRHNiI2JEktTmV3UXVhZHJhdGljR0YlL0kieEdGJTsiIiEiIiQiIiI=Maple can also do reasonably attractive plots very painlessly:QyQtSSVwbG90RzYiNiRJLU5ld1F1YWRyYXRpY0dGJS9JInhHRiU7IiIhIiIlIiIiSome of the good part is not on view, and I like green better than red:QyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiVJLU5ld1F1YWRyYXRpY0dGKC9JInhHRig7ISIjIiIlL0kmY29sb3JHRihJJmdyZWVuR0YoIiIiPlots attributes can also be modified interactively. Right-click on the plot andplay with the available options. See if you can remove the axis labels, make the linemagenta, and change the plot from a line to points.We can put multiple curves on one plot. In order to do this we have to bring in the "plots" package and place the two plots into variables, then use the "display" command.QyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIiQyQ+SSJGRzYiLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYlSS1OZXdRdWFkcmF0aWNHRiUvSSJ4R0YlOyEiIyIiJS9JJmNvbG9yR0YlSSZncmVlbkdGJSIiIg==QyQ+SSJHRzYiLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYlLCRJInhHRiUjIiIiIiIjL0YtOyEiIyIiJS9JJmNvbG9yR0YlSSVibHVlR0YlRi8=QyQtSShkaXNwbGF5RzYiNiM8JEkiRkdGJUkiR0dGJSIiIg==JSFHThis is the end of the intro worksheet (my part of it). Your assignment is to do the following:1. Use a MAPLE command to find 45+3e4+sin(Pi/4)JSFH2. Write a rational expression in which the numerator is a factor of the denominatorJSFH3. Use MAPLE to simplify (reduce) the rational expression in #24. Write an expression in x that uses two out of ln, sin, cos, tan, | |, and square root5. Write a polynomial in x and y, and give it a name. Do NOT print out the result6. Now print your polynomial7. Multiply your polynomial by -3 and add 8 printing the result8. Create a cubic polynomial in x, and give it a name9. Use the solve command to determine if your cubic has any roots10. Differentiate it11. Integrate it from 0 to 212. Plot the cubic, using default colors and line styles13. Create a 4th-degree polynomial in x - give it a different name14. Create a plot in which the cubic appears in a solid blue line, and the quartic in a dashed red lineJSFH