The RawQuery command sends the string query to one of several models from OpenAI, through a Maplesoft server; and returns the response as a string. Most other commands in the NaturalLanguage package are routed through RawQuery, with some pre- and/or post-processing.

Maple can interface with OpenAI's GPT-4o, o1-mini, and o3-mini models. You can select these by using the options $\mathrm{model}=\mathrm{GPT4o}$; $\mathrm{model}=\mathrm{O1Mini}$; and $\mathrm{model}=\mathrm{O3Mini}$, respectively. By default, or when explicitly selected with the $\mathrm{model}=\mathrm{default}$ option, a Maplesoft server chooses an appropriate model. (At the time of release of Maple 2025, this was the o3-mini model.) Note that OpenAI may deprecate and disable models, so the set of models supported may change in the future.

Note: Large language models often generate inaccurate statements. Please keep this in mind: this is not technology for building a bridge with.

$\mathrm{with}\left(\mathrm{NaturalLanguage}\right)\:$

$\mathrm{RawQuery}\left(''Plot\; sin(x)\; in\; maple''\,\mathrm{model}=\mathrm{O1Mini}\right)$

$To plot the sine function \( \sin(x) \) in Maple, you can use the `plot` command, which is a powerful tool for creating graphical representations of mathematical functions. Below are the steps and sample code to help you generate the plot: ## Step-by-Step Guide 1. **Start Maple:** Open your Maple software to access the command interface where you can enter the necessary commands. 2. **Use the `plot` Command:** The basic syntax for plotting a function in Maple is: ```maple plot(function, variable_range); ``` For the sine function, it would look like this: ```maple plot(sin(x), x = a..b); ``` Here, `a` and `b` define the range of the variable \( x \) over which you want to plot the function. 3. **Specify the Range:** It's common to plot trigonometric functions like sine over an interval that covers multiple periods to capture their repeating nature. A typical choice is from \( -2\pi \) to \( 2\pi \). 4. **Enhance the Plot (Optional):** You can add titles, labels, and other styling options to make the plot more informative and visually appealing. ## Sample Maple Code Here's a complete example that plots \( \sin(x) \) from \( -2\pi \) to \( 2\pi \) with additional customization: ```maple # Define the range for x start := -2*Pi: end := 2*Pi: # Plot sin(x) with customization plot(sin(x), x = start..end, title = "Plot of sin(x)", labels = ["x", "sin(x)"], color = blue, thickness = 2, style = line); ``` ### Explanation of the Code: - **Defining the Range:** ```maple start := -2*Pi: end := 2*Pi: ``` These lines set the lower and upper bounds for \( x \) to \( -2\pi \) and \( 2\pi \), respectively. - **Plot Command:** ```maple plot(sin(x), x = start..end, ...) ``` This command tells Maple to plot the sine function within the specified range. - **Customizations:** - `title = "Plot of sin(x)"`: Adds a title to the graph. - `labels = ["x", "sin(x)"]`: Labels the x-axis and y-axis. - `color = blue`: Sets the color of the sine curve to blue. - `thickness = 2`: Makes the curve thicker for better visibility. - `style = line`: Plots the function as a continuous line. ## Result Executing the above code in Maple will generate a graph of \( \sin(x) \) spanning from \( -2\pi \) to \( 2\pi \), complete with axis labels, a title, and a neatly styled sine curve. ## Additional Tips - **Dynamic Exploration:** You can use Maple's interactive features to zoom in and out of different sections of the plot or to explore how changes to parameters affect the graph. - **Multiple Functions:** To plot multiple functions on the same graph, you can list them within the `plot` command. For example: ```maple plot([sin(x), cos(x)], x = -2*Pi..2*Pi, labels = ["x", "Function"], legend = ["sin(x)", "cos(x)"]); ``` - **Exporting the Plot:** After creating the plot, you can export it in various formats (e.g., PNG, PDF) using Maple's export features for use in reports or presentations. By following these steps and utilizing the sample code, you should be able to successfully plot \( \sin(x) \) in Maple and customize it to suit your needs.$

$\mathrm{RawQuery}\left(''maple\; code\; to\; integrate\; (x^2-1)/(x+2)''\,\mathrm{model}=\mathrm{GPT4o}\right)$

$''To\; integrate\; the\; function\; \backslash ((x^2-1)/(x+2)\backslash )\; using\; Maple,\; you\; can\; follow\; these\; steps:\; 1.\; Start\; Maple.\; 2.\; Use\; the\; `int`\; function\; to\; calculate\; the\; integral.\; Here\; is\; the\; Maple\; code\; to\; find\; the\; integral:\; ```maple\; \#\; Define\; the\; function\; f\; :=\; (x^2\; -\; 1)/(x\; +\; 2);\; \#\; Compute\; the\; integral\; integral\; :=\; int(f,\; x);\; \#\; Display\; the\; result\; integral;\; ```\; When\; you\; execute\; this\; code,\; Maple\; will\; compute\; the\; indefinite\; integral\; of\; the\; function\; \backslash ((x^2-1)/(x+2)\backslash )\; with\; respect\; to\; \backslash (x\backslash ).\; Alternatively,\; you\; can\; execute\; the\; integration\; in\; a\; more\; compact\; form\; directly:\; ```maple\; int((x^2\; -\; 1)/(x\; +\; 2),\; x);\; ```\; This\; will\; provide\; the\; same\; result\; when\; you\; run\; it\; in\; Maple.''$

$\mathrm{RawQuery}\left(''Mary\; has\; seven\; apples.\; She\; gives\; two\; to\; Bob\; and\; three\; to\; Sue.\; How\; many\; does\; she\; have\; left?\; Show\; the\; steps''\right)$

$''Step\; 1:\; Mary\; starts\; with\; 7\; apples.\; Step\; 2:\; She\; gives\; 2\; apples\; to\; Bob.\; Now\; she\; has\; 7\; -\; 2\; =\; 5\; apples.\; Step\; 3:\; She\; then\; gives\; 3\; apples\; to\; Sue.\; Now\; she\; has\; 5\; -\; 3\; =\; 2\; apples.\; Final\; Answer:\; Mary\; has\; 2\; apples\; left.''$

$\mathrm{RawQuery}\left(''What\; is\; the\; area\; of\; a\; triangle\; as\; a\; Maple\; equation''\right)$

$''One\; common\; way\; to\; represent\; the\; area\; of\; a\; triangle\; with\; vertices\; (x₁,\; y₁),\; (x₂,\; y₂),\; and\; (x₃,\; y₃)\; in\; Maple\; is\; to\; use\; the\; formula:\; \hspace{1em}\hspace{1em}A\; :=\; 1/2*abs(x1*(y2\; -\; y3)\; +\; x2*(y3\; -\; y1)\; +\; x3*(y1\; -\; y2));\; This\; equation\; computes\; the\; area\; based\; on\; the\; determinant\; of\; a\; matrix\; formed\; by\; the\; coordinates\; and\; then\; taking\; half\; its\; absolute\; value.\; You\; can\; enter\; this\; directly\; into\; Maple\; to\; work\; with\; or\; simplify\; further.''$

$\mathrm{RawQuery}\left(''Can\; you\; explain\; what\; extreme\; value\; analysis\; is?''\right)$

$Extreme value analysis is a statistical approach used to study and model the behavior of the most extreme (i.e., very high or very low) values in a dataset. Instead of focusing on the average or typical observations, it zeroes in on the tails of the probability distribution, which represent rare but potentially impactful events. Here’s a more detailed breakdown: 1. Purpose and Applications:  • It’s particularly useful when you need to understand, predict, or prepare for extreme events such as massive floods, unusually high temperatures, financial crashes, or catastrophic insurance losses.  • The analysis helps in risk management and planning by providing estimates for events that occur very infrequently but have significant consequences. 2. Theoretical Foundation:  • Extreme value theory (EVT) is the mathematical framework underpinning extreme value analysis.  • EVT provides theorems that describe how the distribution of extreme values (for example, the maximum or minimum of a sample) converges to a certain limiting distribution as the sample size increases.  • A key result is the Fisher-Tippett-Gnedenko theorem, which shows that, under mild conditions, the distribution of block maxima converges to one of three types of distributions, often combined into the Generalized Extreme Value (GEV) distribution. 3. Two Main Approaches:  A. Block Maxima Method:   • Data is divided into blocks (e.g., yearly or monthly periods), and the maximum (or minimum) value from each block is collected.   • These extremes are then modeled using the GEV distribution.  B. Peaks Over Threshold (POT) Method:   • Instead of dividing data into blocks, this approach focuses on all observations that exceed a high (or low) threshold.   • The excesses above (or below) the threshold are modeled using the Generalized Pareto Distribution (GPD). 4. Practical Considerations:  • Choosing an appropriate block size or threshold is crucial – too large and you might lose data, too small and you risk including non-extreme events.  • The models hinge on the assumption that extreme events are statistically independent, which often needs to be checked in practice.  • Since extreme events are rare by definition, the available data for analysis is typically sparse, which makes quantifying uncertainty an important part of the analysis. In summary, extreme value analysis provides a toolkit for modeling and forecasting rare events by focusing on the tails of the distribution. This allows analysts and decision-makers in various fields to assess risks associated with extreme phenomena and design strategies to mitigate their potentially severe impacts.$

$\mathrm{RawQuery}\left(''What\text{'}s\; the\; equation\; for\; a\; photovoltaic\; diode?''\right)$

$A common way to model the current–voltage (I–V) behavior of a photovoltaic (PV) diode (i.e. a solar cell) is the “one‐diode” model. In its most comprehensive form, which includes the effects of series (Rₛ) and shunt (Rₛₕ) resistances, the equation is:   I = Iph – I₀ { exp[(q(V + I·Rₛ)/(n·k·T)] – 1 } – (V + I·Rₛ)/Rₛₕ where  • I is the terminal current,  • V is the voltage across the cell,  • Iph is the light-generated (photocurrent),  • I₀ is the diode’s saturation current,  • q is the charge of an electron (approximately 1.602×10⁻¹⁹ coulombs),  • k is Boltzmann’s constant (approximately 1.38×10⁻²³ J/K),  • T is the absolute temperature (in Kelvin),  • n is the ideality factor (typically between 1 and 2),  • Rₛ is the series resistance,  • Rₛₕ is the shunt (parallel) resistance. In many cases, if one assumes an ideal cell (with Rₛ = 0 and Rₛₕ → ∞), the equation simplifies to:   I = Iph – I₀ { exp[(qV)/(n·k·T)] – 1 } This equation represents the balance between the photocurrent generated by the incident light and the diode current described by the Shockley equation. It is the basic equation used to describe how a photovoltaic diode converts light into electrical power, and it forms the basis for more detailed device modeling and simulation.$

The OpenAI website.

The NaturalLanguage:-RawQuery command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.

The NaturalLanguage:-RawQuery command was updated in Maple 2025.